1
-
Upload
jussara-dos-reis -
Category
Documents
-
view
410 -
download
30
Transcript of 1
![Page 1: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1.jpg)
![Page 2: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/2.jpg)
1
P P S S S S ± ± 22001111M M aat t
![Page 3: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/3.jpg)
eemmáát t i i ccaa Prof.: Helder MacedoCCOONNJJ
![Page 4: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/4.jpg)
UUNNTTOOSS1.Conceitos PrimitivosO ponto de partida da teoria dos
![Page 5: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/5.jpg)
conjuntos consistenos seguintes conceitos primitivos: ± conjunto ± elemento de um conjunto ±
![Page 6: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/6.jpg)
igualdade de conjunto2.SubconjuntosConsidere os conjuntos A = {2, 3, 5}, B = {2, 3, 4, 5}e C = {2, 3, 6, 7}. Observe que
![Page 7: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/7.jpg)
todo elemento de A étambém elemento de B. Nessas condições, dizemos queA está contido em B e escrevemos A
![Page 8: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/8.jpg)
B, dizemos aindaque B contém A e escrevemos B
A.Observe também que nem todo
![Page 9: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/9.jpg)
elemento de A éelemento de C, pois 5
A mas 5
C. Nessas condições,dizemos que A
![Page 10: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/10.jpg)
não está contido em C e escrevemos A
C.3.Conjunto das partes de um conjunto:
![Page 11: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/11.jpg)
Considere, por exemplo, o conjunto A = {1,2}. Vamosescrever os subconjuntos de A:y
![Page 12: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/12.jpg)
Com nenhum elemento:J;yCom um elemento: {1}, {2};y
![Page 13: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/13.jpg)
Com dois elementos: {1,2}.O conjunto cujo os elementos são todos ossubconjuntos de A é chamado de
![Page 14: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/14.jpg)
conjunto das partes de Ae geralmente é indicado por P(A). (lê-se P de A).P(A) = {J
![Page 15: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/15.jpg)
, {1},{2},{1,2}}Observe que:J
P(A); {1}
P(A); {2}
P(A)Então
![Page 16: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/16.jpg)
P(A) = 2n
, onde n é o nº de elementos4.Operações com ConjuntosUnião: A
![Page 17: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/17.jpg)
B = {x / x
A ou x
B}Intersecção: A
B = {x / x
A e x
![Page 18: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/18.jpg)
B}Diferença: A ± B = {x / x
A e x
B}Complementar:BAC
![Page 19: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/19.jpg)
BA!
&&2211--8811772266 1 1880055,,&&2266y
![Page 20: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/20.jpg)
Conjunto dos números naturais2= {0, 1, 2, 3, 4, 5, 6, 7, ... }y
![Page 21: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/21.jpg)
Conjunto dos números inteiros>= {... ± 3, ± 2, ± 1, 0, 1, 2, 3, ...}y
![Page 22: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/22.jpg)
Conjunto dos números RacionaisQ = {x / x =q p, p
>e q
![Page 23: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/23.jpg)
>*
}yConjunto dos números irracionaisI = IR ± Qy
![Page 24: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/24.jpg)
Conjunto dos números reaisR = {x / x é racional ou irracional},,1177((5599$$//2266yI
![Page 25: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/25.jpg)
ntervalo Aberto {x
R / 5
x
8} ou ]5, 8[y
![Page 26: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/26.jpg)
I
ntervalo Fechado {x6
/ 5e
xe
![Page 27: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/27.jpg)
8} ou [5, 8]yI
ntervalo Semi-Aberto à Direita {x
R / 5e
![Page 28: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/28.jpg)
x
8} ou [5, 8[yI
ntervalo Semi-Aberto à Esquerda {x
![Page 29: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/29.jpg)
R / 5
xe
8} ou ]5, 8]2->QR o
![Page 30: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/30.jpg)
o
5 85 8yy5 8yo
5 8yo
![Page 31: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/31.jpg)
![Page 32: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/32.jpg)
![Page 33: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/33.jpg)
![Page 34: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/34.jpg)
![Page 35: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/35.jpg)
![Page 36: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/36.jpg)
![Page 37: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/37.jpg)
![Page 38: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/38.jpg)
![Page 39: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/39.jpg)
![Page 40: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/40.jpg)
![Page 41: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/41.jpg)
![Page 42: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/42.jpg)
![Page 43: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/43.jpg)
![Page 44: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/44.jpg)
![Page 45: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/45.jpg)
201. (UFPB)Das afirmações abaixo, destaque a(s)verdadeira(as).I ± Sexe
![Page 46: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/46.jpg)
ysão números naturais quaisquer, entãox± y
![Page 47: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/47.jpg)
é um número natural.II ± Sexé um número racional qualquer ey
![Page 48: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/48.jpg)
umnúmero irracional qualquer, entãox+yé umnúmero irracional.III ± Se
![Page 49: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/49.jpg)
xeysão números reais tais quexy= 1, entãox
![Page 50: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/50.jpg)
= 1 ouy= 1.IV ± Sexeysão números irracionais
![Page 51: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/51.jpg)
quaisquer, entãoo produtoxyé um número irracional.É (são) verdadeira(s)
![Page 52: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/52.jpg)
apenas:a) II c) II e III e) I, II e IV b) III d) I e IV02. (CEFET-06)considerando a figura abaixo comosendo
![Page 53: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/53.jpg)
uma representação dos conjuntos numéricos econsiderando a relação de inclusão entre os mesmos, écorreto
![Page 54: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/54.jpg)
afirmar que os números 1, 2, 3, 4, e 5 podemrepresentar, nesta ordem, os conjuntos:a) IR,>
![Page 55: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/55.jpg)
, IN, Q e C b)>, IN, Q, IR e Cc) IR, IN,>, Q e Cd) IN,>, Q, IR e Ce) IN,
![Page 56: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/56.jpg)
>, IR, Q e C03. (PUC-RS)Sejama, becnúmeros reais, com
![Page 57: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/57.jpg)
abc. O conjunto ]a, c[ ± ]b, c[ é igual ao conjunto:a) {x
![Page 58: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/58.jpg)
R /a
xb} d) {x
R /b
![Page 59: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/59.jpg)
e
xc} b) {x
R /a
x
![Page 60: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/60.jpg)
eb} e) {x
R /b
xec
![Page 61: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/61.jpg)
}c) {x
R /a
xec}04. (Mack-SP)
![Page 62: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/62.jpg)
Se A ={x
2¬x é múltiplo de 11} eB = {x
2¬15
![Page 63: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/63.jpg)
e
xe
187}, o número de elementos deA
![Page 64: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/64.jpg)
B é:a) 16 b) 17 c) 18 d) 19 e) 2005. (UFF-RJ)Dado o conjunto P = {{0}, 0 ,
, {
![Page 65: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/65.jpg)
}},considere as afirmativasI. {0}
PII. {0}
PIII.
![Page 66: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/66.jpg)
PCom relação a essas afirmativas conclui-se que:a) Todas são verdadeiras b) Apenas a I é verdadeirac) Apenas a II é
![Page 67: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/67.jpg)
verdadeirad) Apenas a III é verdadeirae) Todas são falsas06.Sendo A = {
![Page 68: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/68.jpg)
, a, {a,b}}; verifique se são falsas ouverdadeiras cada uma das seguintes proposições:a)
![Page 69: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/69.jpg)
A ( ) f)
A ( ) b){
}
A ( ) g) {
![Page 70: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/70.jpg)
}
A ( )c)a
A ( ) f) {a}
A ( )d){a,b}
![Page 71: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/71.jpg)
A ( ) h) {a,b}
A ( )e){{a, b}}
A ( ) i) {a, {a, b}}
A ( )
![Page 72: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/72.jpg)
07. (Mackenzie)Suponha os conjuntosA = [0, 3]B = ]± g
, 3]C = [± 2, 3]. O conjunto (B ± A)
![Page 73: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/73.jpg)
C é:a)
c) ]± 2, +g
[ e) ]± 2, 3[ b) ]± g
, 0[ d) [± 2, 0[08. (F.M.
![Page 74: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/74.jpg)
I
tajubá-MG)Com relação a parte sombreadado diagrama, é correto afirmar que:a) A ± (B ± C) b) A ± (B
![Page 75: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/75.jpg)
C)c) A ± (B
C)d) A ± (C ± B)e) Nenhuma das respostasanteriores.
![Page 76: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/76.jpg)
09. (UFPE - 97)Numa cidade de 10.000 habitantes sãoconsumidas cervejas de dois tipos A e B. Sabendo
![Page 77: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/77.jpg)
que45% da população tomam da cerveja A, 15% tomamdos dois tipos de cerveja e 20% não toma cerveja,quantos
![Page 78: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/78.jpg)
são os habitantes que não tomam da cervejaB?a) 3.500 c) 4.000 e) 2.000 b) 5.000 d) 4.50010. (PUC-98)
![Page 79: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/79.jpg)
Foram consultadas 1000 pessoas sobre asrádios que costumam escutar. O resultado foi oseguinte: 450 pessoas
![Page 80: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/80.jpg)
escutam a rádio A, 380 escutama rádio B e 270 não escutam A nem B. O número de pessoas que escutam as
![Page 81: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/81.jpg)
rádios A e B éa)100 b) 300 c) 350 d) 400 e) 45011.(PUC-RS)Numa empresa de 90
![Page 82: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/82.jpg)
funcionários, 40 sãoos que falam inglês, 49 os que falam espanhol e 32 osque falam espanhol e não falam inglês. O número de
![Page 83: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/83.jpg)
12345
![Page 84: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/84.jpg)
![Page 85: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/85.jpg)
3funcionários dessa empresa que não falam inglês nemespanhol é:a) 9 b) 17 c) 18 d) 27 e) 89
![Page 86: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/86.jpg)
12. (UFPB-07)Os 40 alunos de uma turma da 4ª sériede uma escola de Ensino Fundamental foram a umsupermerca
![Page 87: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/87.jpg)
do fazer compras. Após 30mi
nutosnosupermercado, a professora reuniu os alunos e
![Page 88: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/88.jpg)
percebeu que exatamente: 19 alunos compraram biscoitos. 24 alunos compraram refrigerantes. 7 alunos não
![Page 89: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/89.jpg)
compraram biscoitos nem refrigerantes.O número de alunos que compraram biscoitos erefrigerantes
![Page 90: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/90.jpg)
foi:a) 17 b) 15 c) 12 d) 10 e) 713. (I
TA-SP)Denotemos por n(X) o número deelementos de
![Page 91: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/91.jpg)
um conjunto finito X. Sejam A, B e Cconjuntos tais quen(AB) = 8,
![Page 92: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/92.jpg)
n(AC) = 9,n(BC) = 10,n
![Page 93: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/93.jpg)
(ABC) = 11 en(A
B
![Page 94: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/94.jpg)
C) = 2.Então,n(A) +n(B) +n(C) é igual a:a)11 b) 14 c)15 d) 18 e) 25
![Page 95: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/95.jpg)
14. (FEI
-SP)Um programa de proteção e preservação detartarugas marinhas, observando
![Page 96: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/96.jpg)
dois tipos decontaminação dos animais, constatou em um de seus postos de pesquisa, que: 88 tartarugas apresentavamsi
![Page 97: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/97.jpg)
nais de contaminação por óleo mineral, 35 nãoapresentavam sinais de contaminação por radioatividade,
![Page 98: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/98.jpg)
77 apresentavam sinais decontaminação tanto por óleo mineral como por radioatividade e 43
![Page 99: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/99.jpg)
apresentavam sinais de apenas umdos dois tipos de contaminação. Quantas tartarugasforam observadas?a) 144 b) 154 c)
![Page 100: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/100.jpg)
156 d) 160 e) 16815.(UFPB-01)A secretaria da Saúde do Estado daParaíba, em estudos
![Page 101: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/101.jpg)
recentes, observou que o númerode pessoas acometidas de doenças como gripe edengue tem assustado bastante a
![Page 102: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/102.jpg)
população paraibana.Em pesquisas realizadas com um universo de 700 pessoas, constatou-se que 10% tiveram gripe e
![Page 103: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/103.jpg)
dengue,30% tiveram apenas gripe e 50% tiveram gripe oudengue. O número de pessoas que tiveram
![Page 104: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/104.jpg)
apenasdengue é:a)350 d) 140 b)280 e) 70c)21016. (UFPB-05)Três instituições de ensino,
![Page 105: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/105.jpg)
aquidenominadas por A, B e C, oferecem vagas paraingresso de novos alunos em seus cursos. Encerradasas inscrições dos
![Page 106: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/106.jpg)
candidatos, verificou-se queexatamente 540 deles se inscreveram para cursos de Ae B, 240 para cursos de A e C, e 180 para os
![Page 107: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/107.jpg)
cursos A,B e C. Quantos candidatos se inscreveram em cursosde A e também em cursos de B ou C?a) 700 d) 500
![Page 108: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/108.jpg)
b) 900 e) 600c) 95017.(UFPB-09)A prefeitura de certa cidade realizou doisconcursos: um para gari e outro para
![Page 109: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/109.jpg)
assistenteadministrativo. Nesses dois concursos, houve um totalde 6.500 candidatos inscritos. Desse total,
![Page 110: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/110.jpg)
exatamente,870 fizeram prova somente do concurso para gari.Sabendo-se que, do total de candidatos inscritos,4.630 não fizeram a
![Page 111: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/111.jpg)
prova do concurso para gari, écorreto afirmar que o número de candidatos quefizeram provas dos dois concursos
![Page 112: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/112.jpg)
foi:a) 4.630 d) 1.740 b) 1.870 e) 1.000c) 1.30018. (UFPB-2010)Antes da realização de uma
![Page 113: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/113.jpg)
campanhade conscientização de qualidade de vida, a Secretariade Saúde de um município fez algumas observações
![Page 114: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/114.jpg)
decampo e notou que dos 300 indivíduos analisados 130eram tabagistas, 150 eram alcoólatras e 40 tinham
![Page 115: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/115.jpg)
essesdois vícios. Após a campanha, o número de pessoasque apresentaram, pelo menos, um dos dois víciossofreu
![Page 116: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/116.jpg)
uma redução de 20%.Com base nessas informações, é correto afirmar que,com essa redução, o número de pessoas sem
![Page 117: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/117.jpg)
qualquer um desses vícios passou a ser:a) 102 b) 104 c) 106 d) 108 e) 11019. (UFCG-06)
![Page 118: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/118.jpg)
Uma escola de Campina grande abriuuma inscrição para aulas de reforço nas disciplinasMatemática, Física e
![Page 119: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/119.jpg)
Química do 2º ano do EnsinoMédio, sem que houvesse coincidência de horários, demodo que permitisse a
![Page 120: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/120.jpg)
inscrição simultânea em maisde uma dessas três disciplinas. Analisando o resultadofinal das inscrições, o coordenador
![Page 121: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/121.jpg)
pedagógicoconstatou:yDos 62 inscritos para as aulas de Física, 22inscreveram-se
![Page 122: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/122.jpg)
exclusivamente para essas aulas;y38 alunos se inscreveram para as aulas deMatemática;y
![Page 123: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/123.jpg)
26 se inscreveram para as aulas de Química;
![Page 124: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/124.jpg)
![Page 125: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/125.jpg)
4yNenhum aluno se inscreveu simultaneamente paraas aulas de Matemática e de Química;y
![Page 126: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/126.jpg)
O número de aluno inscritos exclusivamente para asaulas de Matemática é o dobro do número de alunosinscritos exclusivamente
![Page 127: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/127.jpg)
para as aulas de Química.O número de alunos simultaneamente para as aulasde Matemática e de Física é:a)
![Page 128: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/128.jpg)
26 b) 20 c) 18 d) 24 e) 2201. (UEPB-00)Das alternativas abaixo, assinale acorreta:a) ComoQQ
![Page 129: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/129.jpg)
R R , segue-se que todo número racionalé real. b) Sep
QQ,, entãop
![Page 130: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/130.jpg)
não é um quociente entre doisnúmero inteiros.c) Qualquer que sejaa, b
22
![Page 131: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/131.jpg)
, temos que (a ± b)
22d) Qualquer que sejap, q
>>
![Page 132: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/132.jpg)
, comq{
0, entãoq p
>>.. e) 0,341341...
![Page 133: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/133.jpg)
02. (UEPB-01)Dentre as afirmações abaixo, assinale averdadeira:a) O produto de dois números irracionais é sempreum
![Page 134: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/134.jpg)
número irracional. b) A soma de dois números irracionais nem sempre éum número irracional.c) Todo número
![Page 135: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/135.jpg)
racional é representado por umnúmero decimal exato.d) O quadrado de qualquer número irracional é
![Page 136: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/136.jpg)
umnúmero racional.e) O número real representado por 0,15625 é umnúmero irracional.03. (UEPB-01)Se M = {
![Page 137: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/137.jpg)
x
R R / ± 1xe
4} e N = {x
R R / 2e
![Page 138: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/138.jpg)
x
6}, qual das afirmativas abaixo éverdadeira?a) N ± M = ]4, 6[ d)N M
C
![Page 139: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/139.jpg)
= ]4, 6] b) M ± N = ]±1, 2] e) (M ± N)(N ± M) = 0c) M
N{
![Page 140: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/140.jpg)
N
M04. (UEPB-03)Seja U o conjunto universo de todos osalunos de uma classe
![Page 141: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/141.jpg)
composta por meninos emeninas. Considere agora os seguintes subconjuntosde U:A: conjunto formado pelos
![Page 142: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/142.jpg)
meninos.B: conjunto formado pelos alunos aprovados.Assinale a alternativa que representa o conjunto
![Page 143: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/143.jpg)
A±Ba) Meninas reprovadas. d) Meninos reprovados b) Meninas aprovadas. e) Meninos aprovados.c)
![Page 144: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/144.jpg)
Alunos reprovados.05. (UEPB-99)SeAeBsão conjuntos quaisquer,
![Page 145: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/145.jpg)
então podemos afirmar que:a) A
B =
A =
ou B =
![Page 146: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/146.jpg)
b) A
B
AB = Ac) A
B =
![Page 147: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/147.jpg)
AB =
d) A
B = B
![Page 148: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/148.jpg)
B
Ae) AB = B
A =
06. (UEPB-00)
![Page 149: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/149.jpg)
Dada a inclusão dos seguintes conjuntos:{a, b, c}
X
![Page 150: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/150.jpg)
{a, b, c, d, e}, podemos afirmar que onúmero de conjuntos X é:a) 3 b) 4 c) 5 d) 6 e) 707. (UEPB-00)
![Page 151: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/151.jpg)
Se A e B são disjuntos e não vazios,assinale a alternativa correta.a) A
(AB) d)
![Page 152: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/152.jpg)
(AB) b) B
(A
B) e) (A
![Page 153: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/153.jpg)
B)
Ac) (AA)
B{
(B
![Page 154: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/154.jpg)
B)
A08. (UEPB-00)O conjunto definido por },22)1()1(/{22
!
![Page 155: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/155.jpg)
nnnx xpode ser traduzido como:a) o conjunto vazio. b) o conjunto dos naturais não nulos.c) o
![Page 156: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/156.jpg)
conjunto dos números pares positivos.d) o conjunto dos números ímpares positivos.e) o conjunto dos quadrados dos
![Page 157: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/157.jpg)
números naturais.09. (UEPB-06)O quadro abaixo mostra o resultado deuma pesquisa realizada com
![Page 158: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/158.jpg)
1.800 pessoas,entrevistadas a respeito da audiência de três programasfavoritos de televisão, a
![Page 159: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/159.jpg)
saber: Esporte (E), Novela (N)e Humorismo (H).ProgramasE N H E e N N e H E e H E, N e H Nº deEntrevistados
![Page 160: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/160.jpg)
400 1.220 1.080 220 800 180 100
![Page 161: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/161.jpg)
![Page 162: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/162.jpg)
![Page 163: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/163.jpg)
![Page 164: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/164.jpg)
![Page 165: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/165.jpg)
5
![Page 166: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/166.jpg)
De acordo com os dados apresentados, o número de pessoas entrevistadas que não assistem a algum dos três
![Page 167: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/167.jpg)
programas é:a) 900 c) 100 e) 400 b) 200 d) 30010. (UEPB-01)Numa pesquisa de rua sobre a prefe-rência musical entre
![Page 168: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/168.jpg)
axé-music e forró, forma feitasduas perguntas: Você gosta de forró?Você gosta deaxé? A coleta dos dados está
![Page 169: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/169.jpg)
apresentada no seguintehistograma:Com base no gráfico, o total de pessoa que parti-cipouda entrevista foi:a) 572 pessoas. d)
![Page 170: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/170.jpg)
1244 pessoas. b) 610 pessoas. e) 884 pessoas.c) 1206 pessoas.11. (UEPB-07)Uma determinada cidade
![Page 171: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/171.jpg)
organizou umaolimpíada de matemática e física, para os alunos do 3ºano do ensino médio local. Inscreveram-se
![Page 172: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/172.jpg)
365 alunos. No dia da aplicação das provas, constatou-se que 220alunos optaram pela prova de matemática,
![Page 173: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/173.jpg)
180 pela defísica, 40 por física e matemática; alguns, por motivos particulares, não compareceram
![Page 174: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/174.jpg)
ao local de provas.Então, o número de alunos que não compareceram às provas foi:a) 35 b) 5 c) 15 d) 20 e) 10
![Page 175: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/175.jpg)
FFUUNNÇÇÕÕEESSO Conceito Matemático de Função:Como, em geral, trabalhamos
![Page 176: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/176.jpg)
com funções numéricase, podemos definir o que é uma função matemáticautilizando a linguagem da teoria dos
![Page 177: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/177.jpg)
conjuntos.Para isso, temos que definir antes o que é produtocartesiano e o que é uma relação entre dois conjuntos.
![Page 178: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/178.jpg)
Produto CartesianoDados dois conjuntos não vaziosAeB, denomina-se
![Page 179: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/179.jpg)
produto cartesi
ano(indica-se por AX
B) deApor B
![Page 180: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/180.jpg)
oconjunto formado pelos pares ordenados nos quais o primeiro elemento pertence aA
![Page 181: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/181.jpg)
e o segundo pertence aB.AX
B = {(x, y)¶x
![Page 182: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/182.jpg)
A e y
B}RelaçãoDados dois conjuntosAeB
![Page 183: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/183.jpg)
, dá-se o nome de rela-çãoRdeAemB
![Page 184: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/184.jpg)
a qualquer subconjunto de AX
B.Ré uma relação deA
![Page 185: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/185.jpg)
emBRAXBD
![Page 186: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/186.jpg)
efinição de FunçãoA função pode ser definida como um tipo especial derelação:Sejam dois
![Page 187: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/187.jpg)
conjuntos não vazios ef uma relação deAemB. Essa relaçãof
![Page 188: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/188.jpg)
é uma função deAemBquando acada elementoxdo conjunto
![Page 189: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/189.jpg)
Aestá associado a um esomente um elementoydo conjuntoB.A definição acima nos diz
![Page 190: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/190.jpg)
que para uma relaçãof deAemBser considerada uma função, é
![Page 191: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/191.jpg)
preciso satisfazer duas condições:
Todo elemento deAdeve estar associado a
![Page 192: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/192.jpg)
algumelemento deB.
A um dado elemento deA
![Page 193: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/193.jpg)
deve estar associado umúnico elemento deB.NotaçãoQuando temos uma função
![Page 194: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/194.jpg)
f deAemB, podemosrepresenta-la da seguinte forma:
![Page 195: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/195.jpg)
f :ApB(lê-se: função deAem
![Page 196: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/196.jpg)
B)A letraf , em geral, dá o nome às funções, mas podemos ter também a função
![Page 197: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/197.jpg)
g ,h etc. Assim, por exemplo, escrevemosg :A
![Page 198: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/198.jpg)
pBpara designar a funçãog deAemB.
![Page 199: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/199.jpg)
Quando representamos a função pela sua fórmula (leide associação), podemos ainda utilizar uma
![Page 200: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/200.jpg)
notaçãodiferente.
Se a fórmula for y=x
![Page 201: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/201.jpg)
+ 5, podemos escrever tambémf (x) =x+ 5.
![Page 202: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/202.jpg)
O símbolof (x), lê-sef dex
![Page 203: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/203.jpg)
, tem o mesmo significadodoye pode simplificar a linguagem. Por exemplo, emvez de dizermos:
![Page 204: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/204.jpg)
qual o valor deyquandox=2?,dizemos simplesmentequal o valor de
![Page 205: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/205.jpg)
f (2). Assim,f (2)significa o valor deyquandoxé 2.
![Page 206: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/206.jpg)
Domínio ( D)é o conjunto dos valores de x para osquais f(x) existe e é um número real.
![Page 207: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/207.jpg)
I magem ( I m)é o conjunto dos valores de f(x)associados a
![Page 208: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/208.jpg)
pelo menos um x, xD
.
![Page 209: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/209.jpg)
![Page 210: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/210.jpg)
E studo doDomínio de uma FunçãoQuando definimos uma função, o domínioD
![Page 211: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/211.jpg)
, que é oconjunto de todos os valores possíveis da variávelindependentex. A condição de existência de
![Page 212: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/212.jpg)
uma funçãoreal depende do tipo da função a ser analisada. Vamosanalisar os casos de funções abaixo:
![Page 213: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/213.jpg)
Função Polinomialf (x) =ax+
![Page 214: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/214.jpg)
b@função polinomial do 1º grau.f (x) = a
![Page 215: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/215.jpg)
x2
+bx+ c@função polinomial do 2º grau.
![Page 216: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/216.jpg)
f (x) = ax3
+bx2
![Page 217: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/217.jpg)
+ cx+ d @função polinomial do 3º grauO domínioD
![Page 218: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/218.jpg)
das funções polinomiais é sempre oconjunto dos números.
Função Fracionária)(
![Page 219: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/219.jpg)
xN
xf !px{
0, ou seja, denominador
![Page 220: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/220.jpg)
deveser diferente de zero.
Função Irracionalpar
)(x xf
![Page 221: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/221.jpg)
!
pxu0, o radicando deve ser maior ou igual a zero.ímpar
)(
![Page 222: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/222.jpg)
x xf !px= IR, o radicando pode ser qual-quer número real.
![Page 223: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/223.jpg)
par
)(x N xf !
px"
![Page 224: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/224.jpg)
0, o radicando deve ser maior que zero.ímpar
)(xN
xf !
![Page 225: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/225.jpg)
px{
0, radicando deve ser diferentede zero.CONCLUSÃO:
![Page 226: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/226.jpg)
f (x) =pol i
nomi
al D
![Page 227: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/227.jpg)
= IR )(xN
xf !D
= IR *
![Page 228: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/228.jpg)
par
)(x xf !D
= IR +ímpar
)(
![Page 229: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/229.jpg)
x xf !D
= IR par
)(x N xf !
![Page 230: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/230.jpg)
D
= IR *ímpar
)(x N xf !D
![Page 231: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/231.jpg)
= IR *
20. (UFV)Os pares ordenados (1,2), (2,6), (3,7), (4,8) e(1,9) pertencem ao
![Page 232: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/232.jpg)
produto cartesiano A x B Sabendo-se que AxB tem 20 elementos, é correto afirmar que asoma dos
![Page 233: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/233.jpg)
elementos de A é:a) 9 b) 11 c) 10 d) 12 e) 1521. (PUC-SP)Os pares ordenados (2, 3), (3, 3) e (1, 4)são elementos do conjunto A
![Page 234: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/234.jpg)
xB. Então:a)(1,3), (2,4) e (3,4) estão necessariamente em AxB b) (1,1), (1,3), (2,2),
![Page 235: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/235.jpg)
(2,4) e (3,4) estão necessária-mente em A x B.c)(1,1), (2,2) e (4,4) estão necessariamente em Ax
![Page 236: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/236.jpg)
Bd) (3,2) e (4,1) estão necessariamente em A x B.e) Os elementos dados podem ser os únicos de AxB22. (UFPB)
![Page 237: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/237.jpg)
Dado o conjunto A = {1, 2, 3, 4} qual dasrelações abaixo, definida de A em A, representa
![Page 238: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/238.jpg)
umafunção?a) {(1,1), (2,2), (2,3), (2,4)} b) {(1,2), (2,3), (3,2), (4,2)}c) {(1,1), (1,2), (2,3), (4,1)}d) {(1,2), (3,4), (3,2), (4,4)}e)
![Page 239: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/239.jpg)
{(4,1), (3,2), (2,2), (2,3)}23. (UFCE)Sejam:A = { 2, 4, 6, 8, 10, 12, ..., 62, 64} eB = {(m, n)
![Page 240: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/240.jpg)
A x A | m + n = 64}O número de elementos de B é igual a:a) 31 b) 32 c) 62 d) 64 e) 12824. (Puc-MG)Dos gráficos, o único que
![Page 241: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/241.jpg)
representa umafunção de domínio_ a11/eexx
e imagem
![Page 242: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/242.jpg)
_ a3
1/eeyy
é:
![Page 243: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/243.jpg)
![Page 244: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/244.jpg)
![Page 245: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/245.jpg)
![Page 246: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/246.jpg)
![Page 247: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/247.jpg)
![Page 248: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/248.jpg)
7
![Page 249: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/249.jpg)
25. (UFPB-05)Sejam A = {x
IR / 0exe
2} eB = {x
IR / 0
![Page 250: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/250.jpg)
exe
3}. Quantos pares ordenados,cujas coordenadas são todas inteiras,
![Page 251: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/251.jpg)
existem no produto cartesiano AxB?a) 12 b) 10 c) 9 d) 8 e) 626.
![Page 252: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/252.jpg)
Ache o domínio das funções:a) f(x ) =2xx7x413x1x
b) y =1x26x1
27. (UERN)
![Page 253: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/253.jpg)
Seja f : DpIR, D
IR, a função definida por f(x) =1x1x5
![Page 254: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/254.jpg)
. O domínioD
da função pode ser descrito por:a) [± 1, 5] d) ] ± 1,5] b) [5,g
] e) ]5,g
![Page 255: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/255.jpg)
[ ± {± 1}c) ]5,g
[28. (U.Potiguar-RN)O domínio da função3
![Page 256: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/256.jpg)
142)(x x x x xf !é igual a:a){x
R
![Page 257: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/257.jpg)
xe
0} d) {x
R
xu1} b)
![Page 258: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/258.jpg)
{x
R
xu0} e) {x
R
![Page 259: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/259.jpg)
xu± 1c){x
R
xe
![Page 260: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/260.jpg)
± 1}29. (UFPB-03)Em uma viagem de carro de João Pessoaa Recife, o motorista de lotação Sérgio sabe que, do
![Page 261: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/261.jpg)
ponto de partida ao de chegada, o percurso total é de150k m
, sendo que 120k m
![Page 262: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/262.jpg)
são percorridos na estrada eo restante, na cidade. Se o carro faz 10k m
por litros nacidade, 12k
![Page 263: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/263.jpg)
m
por litro na estrada, e o preço docombustível é de R$ 1,85 por litro, então Sérgiogastará com o
![Page 264: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/264.jpg)
combustível, nessa viagem, aimportância de:a) R$ 18,50 d) R$ 24,99 b) R$ 23,12 e) R$ 27,75c) R$ 24,0530. (UEL-PR)
![Page 265: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/265.jpg)
Seja a funçãof (x) =ax3
+b
![Page 266: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/266.jpg)
.Se f(± 1) = 2 ef(1) = 4, entãoaebvalem, respectivamente:a) ± 1 e ± 3 d) 3 e ± 1 b) ± 1 e
![Page 267: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/267.jpg)
3 e) 3 e 1c) 1 e 331.(UFOP-MG)Seja a funçãof : IR pIR, dada por:
![Page 268: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/268.jpg)
±°±¯®!x x x xf 51510)(2
Então, o valor de
![Page 269: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/269.jpg)
¹¹ º ¸©©ª¨22222f f f
![Page 270: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/270.jpg)
é umnúmero:a)inteiro d) ímpar b)par e) irracionalc)racional32. (UFRN)Dada a função f :
![Page 271: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/271.jpg)
>p>, definida para todointero n
>, tal que f(0) = 1 e f(n +1) =
![Page 272: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/272.jpg)
f(n) + 2 podemos afirmar que o valor de f(200) é:a) 201 b) 203 c) 401 d) 403 e) 60233. (UFPB-04)
![Page 273: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/273.jpg)
Na figura abaixo, está representado ográfico de uma funçãof :[± 2,
![Page 274: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/274.jpg)
2]pIR.O número de soluções da equaçãof( x)=
![Page 275: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/275.jpg)
2éa) um c) três e) cinco b) dois d) quatro34.(UFPB)Considere as funçõesf
![Page 276: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/276.jpg)
eg de IR em IR definidas por:±°±¯®u
!°¯®u
![Page 277: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/277.jpg)
!0xse, 0xse, e 0xse0xse2)1()(,52),2()(x xf xg x x
![Page 278: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/278.jpg)
g xf
, entãof (± 3) vale:a) ± 2 b) 0 c) 5 d) ± 5 e) 1se x
± 1se ± 1
![Page 279: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/279.jpg)
exe
1se x"1
![Page 280: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/280.jpg)
![Page 281: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/281.jpg)
![Page 282: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/282.jpg)
![Page 283: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/283.jpg)
8
![Page 284: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/284.jpg)
35.Considere a função y = f(x), que tem como domínio ointervalo {x
![Page 285: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/285.jpg)
: ± 2 < x 3} e que se anula somenteem x = ±3/2 e x = 1, como se vê nesta figura:Considere as afirmações
![Page 286: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/286.jpg)
abaixo sobre f:I. f é crescenteII. f decresce com xIII. f(1/2) = f(2)IV. f(x) 0
![Page 287: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/287.jpg)
x ± 3/2Então, a seqüência correta é:a) F F F F d) V F V F b) F V V V e) F V V Vc) V V V V01. (UEPB-06)
![Page 288: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/288.jpg)
Dados os conjuntosA = {-1, 0, 1, 2} e B = {-1, 0, 1, 2, 3, 5, 8) e asrelaçõesR = { (x,
![Page 289: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/289.jpg)
y)
AxB /y=x1
![Page 290: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/290.jpg)
}S = { (x,y)
AxB /y
![Page 291: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/291.jpg)
=x
²}T = { (x,y)
![Page 292: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/292.jpg)
AxB /y=x
²+ 1 }U = { (x
![Page 293: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/293.jpg)
,y)
AxB /y=x
![Page 294: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/294.jpg)
³}a alternativa correta é:a) apenas uma das quatro relações é função de A em B b) apenas duas das quatro
![Page 295: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/295.jpg)
relações são funções de Aem Bc) apenas três das quatro relações são funções de A emBd) todas as quatro relações são
![Page 296: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/296.jpg)
funções de A em Be) nenhuma das quatro relações é função de A em B02. (UEPB-03)Em uma indústria de
![Page 297: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/297.jpg)
autopeças, o custode produção de peças é de R$ 12,00 fixo mais umcusto variável de R$ 0,70 por cada unidade produ-
![Page 298: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/298.jpg)
zida. Se em um mês foram produzidasxpeças, então alei que representa o custo total dessas
![Page 299: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/299.jpg)
xpeças é:a)f (x) = 0,70 ± 12xd)f
![Page 300: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/300.jpg)
(x) = 0,70 + 12xb)f (x) = 12 ± 0,70
![Page 301: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/301.jpg)
xe)f (x) = 12x0,70x
![Page 302: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/302.jpg)
c)f (x) = 12 + 0,70x03. (UEPB-99)O diagrama abaixo
![Page 303: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/303.jpg)
representa umarelaçãof deAemB.Para que a relação
![Page 304: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/304.jpg)
f seja uma função deAemB, basta:a) apagar a seta 4 e retirar o
![Page 305: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/305.jpg)
elemento K. b) retirar os elementos K e T.c) apagar a seta 2 e retirar o elemento K.d) apagar as setas 2 e 4.e)
![Page 306: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/306.jpg)
retirar o elemento K.04.(UEPB-00)O tanque de combustível de umautomóvel tem capacidade para 60 litros
![Page 307: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/307.jpg)
de gasolina,entretanto dispomos apenas de 25% dessa capaci-dadede combustível. Se esse automóvel tem
![Page 308: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/308.jpg)
um consumomédio de 4/5 litros de gasolina por quilômetro rodado,a fórmula que relaciona a quanti-dade Q,
![Page 309: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/309.jpg)
em litros, decombustível no tanque em fun-ção do quilômetro K rodado será representado por:a) Q = 15 ± K d) Q = ¼ ±
![Page 310: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/310.jpg)
0,8K b) Q = 15 + 0,8K e) Q = 15 ± 0,8K c) Q = ¼ + 0,8K 05. (UEPB-06)O número do telefone residencial deRebeca é
![Page 311: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/311.jpg)
9374182e do comercial é tal que°¯®e"!7,17,)(
![Page 312: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/312.jpg)
sex xsex x xf ondexé algarismo do telefone residencial.
![Page 313: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/313.jpg)
Dessaforma, a soma dos algarismos que compõem o telefonecomercial será:a) 29 c) 27 e) 26 b) 28 d) 3006. (UEPB-09)
![Page 314: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/314.jpg)
O domínio da função11)(!
x x xf édado por:a) D = {x
IR
![Page 315: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/315.jpg)
x 1} b) D = {x
IR
x
± 1ou x 1}
![Page 316: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/316.jpg)
![Page 317: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/317.jpg)
![Page 318: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/318.jpg)
![Page 319: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/319.jpg)
![Page 320: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/320.jpg)
![Page 321: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/321.jpg)
9
![Page 322: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/322.jpg)
xyxyxyxc) D = {x
IR
![Page 323: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/323.jpg)
x
± 1ou x"1}d) D = {x
IR
![Page 324: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/324.jpg)
x ± 1ou x 1}e) D = {x
IR
x"1}07. (UEPB-99)
![Page 325: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/325.jpg)
Considere a função realy=f (x), cujográfico está
![Page 326: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/326.jpg)
representado a seguir. Assinale aalternativa correta:a) A função é decrescente no intervalo [x3
![Page 327: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/327.jpg)
, x5
] b)f (0) = 0c) A função é decrescente no intervalo [x3
![Page 328: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/328.jpg)
, x5
]d)f (x1
) =f (x3
![Page 329: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/329.jpg)
) =f (x5
) = 0e)f (x2
) =f
![Page 330: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/330.jpg)
(x4
) = 008. (UEPB-00)Numa loja de artefatos de couro, osalário mensal fixo de um vendedor é
![Page 331: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/331.jpg)
de um saláriomínimo (salário mínimo atual no país R$ 136,00). Por cada unidade vendida, o vendedor
![Page 332: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/332.jpg)
ganha 3 reais decomissão. O número de unidades que o vendedor deverá vender para atingir um salário mensal de 700reais será
![Page 333: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/333.jpg)
de :a) 290 b) 280 c) 272 d) 270 e) 18809. (UEPB-09)Uma função real f(x) satisfaz às con-dições: f(x + y) = f(x) + f(y)
![Page 334: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/334.jpg)
para todo x e y reais,f(1) = 3 e f
5= 4. O valor de f
![Page 335: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/335.jpg)
52
é:a) 9 b) 10 c) 8 d) 12 e) 1610. (UEPB-09)As funções f(x) = x
![Page 336: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/336.jpg)
2
+ mx + 1 e g(x) = x2
+ 4x + n satisfazem à condição 4f(x) = g(2x) + 1 paratodo x real.
![Page 337: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/337.jpg)
O valor de 3m + 2n é:a) 10 b) 13 c) 12 d) 14 e) 1511. (UEPB-99)Estima-se que a população de camarõesconfinados em um
![Page 338: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/338.jpg)
viveiro, para daqui a t anos, sejadado por 3410212)(!t t t
![Page 339: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/339.jpg)
f cabeças por m3
do viveiro. A estimativa da populaçãode camarões ao final do
![Page 340: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/340.jpg)
primeiro ano será dada por f (1), ao final do segundo ano por f (2), e assimsucessiva
![Page 341: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/341.jpg)
mente. Portanto, o aumento da população decamarões, apenas no segundo ano, será de:a)
![Page 342: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/342.jpg)
15750 cabeças por m3
. b) 16000 cabeças por m3
.c) 15500 cabeças por m3
![Page 343: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/343.jpg)
.d) 500 cabeças por m3
.e) 250 cabeças por m3
.FFuunnççããoo
![Page 344: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/344.jpg)
II
nn j jeettoorraaUma função f : ApB é dita injetora se, e somente se,
![Page 345: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/345.jpg)
x1{
x2
f(x1
){
![Page 346: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/346.jpg)
f(x2
) para todox1
ex2
do conjunto A.
![Page 347: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/347.jpg)
FFuunnççããooSSoobbrree j jeettoorraaUma função f : Ap
![Page 348: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/348.jpg)
B é dita sobrejetora se, e somentese, o seu conjunto imagem for igual ao seucontradomínio, ou seja,I
![Page 349: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/349.jpg)
m = BFFuunnççããooBBii j jeettoorraaUma função f : Ap
![Page 350: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/350.jpg)
B é dita bijetora se, e somente se,ela for injetora e sobrejetora.FFuunnççããooPPaarr
![Page 351: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/351.jpg)
As funções cujos gráficos formam figuras simétricasem relação ao eixo de simetria, no caso o eixo dasordenadas (e
![Page 352: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/352.jpg)
i
xo Y ).Função Par é uma funçãoy=f (x
![Page 353: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/353.jpg)
) tal que,f (x) =f (± x) para todo
![Page 354: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/354.jpg)
xpertencente ao seu domínio.FFuunnççããooÍÍmmppaarr As funções cujos gráficos formam figuras
![Page 355: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/355.jpg)
simétricasem relação à origem, ponto0de coordenadas (0, 0).y
![Page 356: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/356.jpg)
![Page 357: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/357.jpg)
![Page 358: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/358.jpg)
![Page 359: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/359.jpg)
![Page 360: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/360.jpg)
10
ymnm pqnypqyyyy
![Page 361: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/361.jpg)
f g hFunção ímpar é uma funçãoy=f (
![Page 362: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/362.jpg)
x) tal que,f (± x) = ± f (x
![Page 363: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/363.jpg)
) para todoxpertencente ao seu domínio.Conclusão:Sef f ((x x
![Page 364: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/364.jpg)
))==± ± f f ((x x)) f f ((x x))éép paar r ..
![Page 365: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/365.jpg)
S
ef f (( ± ± x x))==± ± f f ((x x))
![Page 366: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/366.jpg)
f f ((x x))ééíímm p paar r .. Obs:Asf unções, e
![Page 367: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/367.jpg)
m
g eral, que não sãof unções paresnem
f unções í m
pares são cham
![Page 368: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/368.jpg)
adas def unções sem
par i
dade.
FFuunnççããoo
![Page 369: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/369.jpg)
II
nnvveerrssaaSe f : ApB é uma função bijetora, então existe umaúnica função g
![Page 370: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/370.jpg)
:BpA tal que g(b)= af(a) = b paratodo a
![Page 371: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/371.jpg)
A e b
B. A função g é chamada inversa de f eserá indicada por f ± 1
![Page 372: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/372.jpg)
.Da definição decorre que os gráficos de f e de f ± 1
sãosimétricos em relação à bissetriz do 1º e 3º
![Page 373: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/373.jpg)
quadrantes.Assim:FFuunnççããooCCoommppoossttaaVamos pensar na função
![Page 374: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/374.jpg)
f de IR em IR definida pelalei f(x)=x + 1.Entãof leva cada x real ao número x + 1Em seguida,
![Page 375: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/375.jpg)
pensemos na funçãog de IR em IR definida pela lei g(x) = x2
. Sabemos queg
![Page 376: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/376.jpg)
leva cada xreal ao número x2
.Qual será o resultado final se tomarmos emx
![Page 377: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/377.jpg)
real e aele aplicarmossucessi
vam
entea lei def e a lei de
![Page 378: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/378.jpg)
g ?Teremos:x x + 1 (x + 1)2
O resultado final é quexé levado a (x + 1)2
![Page 379: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/379.jpg)
. Essafunçãohde IR em IR que levaxaté (x + 1)2
é chamadocom
![Page 380: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/380.jpg)
postadeg comf .Indica-seh =g S
f
![Page 381: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/381.jpg)
(Lê-se g bola f´), tal que h(x) =(gS
f)(x) = g(f(x)).36.(UFF)Considere as funções
![Page 382: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/382.jpg)
f ,g eh, todas definidasde [m, n] em [p, q] representadas
![Page 383: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/383.jpg)
através dos gráficosabaixo:a)f é injetiva,g é sobrejetiva ehnão é injetiva b)
![Page 384: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/384.jpg)
f é sobrejetiva,g é injetiva ehnão é sobrejetiva.c)f não é injetiva,
![Page 385: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/385.jpg)
g é bijetiva ehé injetiva.d)f é injetiva,g não é sobrejetiva e
![Page 386: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/386.jpg)
hé injetivae)f é sobrejetiva,g não é injetiva ehé sobrejetiva.37.
![Page 387: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/387.jpg)
Seja f : {1, 2, 3, 4, 5}p{1, 2, 3, 4, 5} uma funçãoinjetiva, satisfazendo:f(1), f(2)
![Page 388: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/388.jpg)
{1, 2}f(3)
{2, 4}f(4)
{1, 4, 5}.Então f(5) é igual a:a) 1 b) 2 c) 3 d) 4 e) 538.(UFPB)
![Page 389: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/389.jpg)
A={3
, ± 2, ± 1, 0, 1, 2,3}, B = {1, 2,4, 5} ef
![Page 390: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/390.jpg)
:ApB definida por f (x) =x
![Page 391: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/391.jpg)
2
+ 1. pode-seafirmar quef é uma função:a) injetora e ímpar d) injetora e par b)
![Page 392: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/392.jpg)
sobrejetora e par e) sobrejetora e ímpar c) bijetora39.(PUC-Camp)Seja f a função de IR em IR,
![Page 393: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/393.jpg)
dada pelográfico a seguir:É correto afirmar que:a) f é sobrejetora e não injetora. b) f é bijetora.c)
![Page 394: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/394.jpg)
f(x) = f(± x) para todo x real.f f ±
f gsomar 1uadrar
![Page 395: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/395.jpg)
![Page 396: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/396.jpg)
![Page 397: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/397.jpg)
![Page 398: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/398.jpg)
![Page 399: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/399.jpg)
![Page 400: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/400.jpg)
![Page 401: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/401.jpg)
![Page 402: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/402.jpg)
11
![Page 403: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/403.jpg)
d) f(x) > 0 para todo x real.e) o conjunto imagem de f é ] -g
; 2 ].40. (PUCMG-2001)
![Page 404: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/404.jpg)
Considere a função f : IR pIR definida por:f(x) = ¡
¢ £
0¤
s¥
,¤
![Page 405: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/405.jpg)
20¤
s¥
,¤
22
. O valor da expressãof[f(1)] ± f[f(3)] é:a) 5
![Page 406: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/406.jpg)
b) 6 c) 7 d) 8 e) 941. (UERN)As funçõesf eg são definidas por
![Page 407: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/407.jpg)
f (x) = x ± 1 eg (x) = x2
± 3x + 2. Calculando-seg (f
![Page 408: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/408.jpg)
(x)) tem-se:a) x2
± 2x + 1 d) x2
± 5x + 6 b) x2
± 3x + 1 e) x3
± 5x2
![Page 409: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/409.jpg)
+ 5x ± 2c) x2
± 3x + 142. (UFPB)Sef (x) = 2x + 5 ef (
![Page 410: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/410.jpg)
g (x)) = 2x2
± 6x
![Page 411: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/411.jpg)
+ 5,então, pode-se afirmar que:a)g (x) =x2
![Page 412: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/412.jpg)
± 3xd) g(x) =x2
± 3x+ 1, b)g
![Page 413: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/413.jpg)
(x) =x2
± 6x+ 5 e) g(x) = 3x2
± 2
![Page 414: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/414.jpg)
xc)g (x) =f (x
![Page 415: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/415.jpg)
)43.(PUC-MG)Dadosg (x) = 5x2
+ 3 e (g
![Page 416: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/416.jpg)
of )(x) =5x±7 odomínio def (x) é:a) {x
IR ¹
![Page 417: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/417.jpg)
xu2} d) {x
IR ¹xe
2} b) {x
![Page 418: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/418.jpg)
IR ¹0
xe
53} e) {x
![Page 419: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/419.jpg)
IR ¹xe
± 2}c) {x
IR ¹x
![Page 420: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/420.jpg)
u57}44. (UEPB-00)Sejaf a função real definida por f
![Page 421: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/421.jpg)
(x) =212x x
, com x{
2. Entãof (f
![Page 422: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/422.jpg)
(x)) é dada por:a)122x x
b) 1 c) x d)2212¹ º ¸©ª¨
![Page 423: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/423.jpg)
x x
e)212x x
45. (MAQUENZI
E
![Page 424: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/424.jpg)
)No esquema acima,f eg são funções,respectivament
![Page 425: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/425.jpg)
e, de A em B e de B em C. Então:a)g (x) = 6x + 5 d)f (x) = 8x + 6 b)f (x) = 6x + 5 e)
![Page 426: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/426.jpg)
g (x) =21xc)g (x) = 3 x + 2
![Page 427: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/427.jpg)
46. (Uniube-MG)SejaK
uma constante real,f eg
![Page 428: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/428.jpg)
funções definidas em IR tais quef (x) =K
x + 1 eg (x) = 13x +K
![Page 429: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/429.jpg)
. Os valores deK
que tornam aigualdadef S
g =g S
![Page 430: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/430.jpg)
f verdadeira é:a) ± 3 ou 3 d) ± 3 ou 4 b) ± 4 ou 4 e) ± 4 ou ± 3c) ± 4 ou 347. (USF-SP)Sef
![Page 431: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/431.jpg)
(x) =x± 1eg (f ± 1
![Page 432: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/432.jpg)
(x)) = x + 2, entãog (1) é igual a:a) 2 b) 1 c) ± 1 d) 0 e) ± 248. (UN
![Page 433: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/433.jpg)
I
-R I
O)A função inversa da função bijetoraf : IR ± {4}
![Page 434: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/434.jpg)
pIR ± {2} definida por f (x) =4x3x2é:a)
![Page 435: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/435.jpg)
3x24x1
!f d)2x3x41
![Page 436: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/436.jpg)
!f b)3x24x1!
![Page 437: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/437.jpg)
f e)2x3x41
!f c)
![Page 438: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/438.jpg)
x23x41!f 49. (UFRJ)O valor real dea
![Page 439: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/439.jpg)
para queax x xf
!21)(
![Page 440: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/440.jpg)
possua como inversa a função1231)(1!x x xf
![Page 441: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/441.jpg)
é:a) 1 b) 2 c) 3 d) 4 e) 550. (MACK-SP)Sex"1 ef
![Page 442: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/442.jpg)
(x) =1x x, então o valor def
![Page 443: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/443.jpg)
(f (x+ 1) é igual a :a)x+ 1 d)1
![Page 444: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/444.jpg)
x xb)11xe)11
![Page 445: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/445.jpg)
x xc)x± 151. (UFPB-00)Considere a função g : Ap
![Page 446: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/446.jpg)
A, ondeA = {1, 2, 3, 4}. Sabendo-se que g(1) = 2, g(2) = 1 eque g possui inversa, então é correto afirmar:a)g(x) = x,
![Page 447: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/447.jpg)
x
A b)g(g(x)) = x,
x
Ac)
![Page 448: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/448.jpg)
g(g(x)) = g(x),
x
Axyy2x+1
![Page 449: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/449.jpg)
yx+5f g
![Page 450: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/450.jpg)
![Page 451: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/451.jpg)
![Page 452: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/452.jpg)
![Page 453: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/453.jpg)
![Page 454: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/454.jpg)
![Page 455: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/455.jpg)
![Page 456: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/456.jpg)
![Page 457: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/457.jpg)
d)g(3) = 1 e g(4) = 2e)g(g(1)) = 2 e g(g(2)) = 152. (UFPB-04)
![Page 458: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/458.jpg)
Na figura abaixo está representado ográfico de uma função]5,1[]3,3[:p
f
![Page 459: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/459.jpg)
.É verdade quea) A função) x( f
não possui inversa. b)A função) x( f
![Page 460: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/460.jpg)
possui inversa, cujo gráfico estárepresentado na figura a seguir.c)A função) x( f
![Page 461: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/461.jpg)
possui inversa, cujo gráfico estárepresentado na figura a seguir.d)A função) x( f
![Page 462: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/462.jpg)
possui inversa, cujo gráfico estárepresentado na figura a seguir.e)A função) x( f
![Page 463: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/463.jpg)
possui inversa, cujo gráfico estárepresentado na figura a seguir.53. (UFPB-05)
![Page 464: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/464.jpg)
Considere a função invertívelf : IR pIR definida por f (
![Page 465: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/465.jpg)
x)=2x+ b, ondeb
![Page 466: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/466.jpg)
é uma constanteSendof ±1
(x) a sua inversa, qual o valor deb
![Page 467: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/467.jpg)
, sabendo-se que o gráfico def ±1
passa pelo ponto A(1, ± 2)?a) ± 2 b) ± 1 c) 2 d) 3 e) 554. (UFPB-06)
![Page 468: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/468.jpg)
Considere a função]3,0[ ]2,0[ :
pf ,definida por:±°±¯®eee
![Page 469: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/469.jpg)
!2112102
x ,x x ,x )x ( f A função inversa def está melhor representada nográfico:
![Page 470: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/470.jpg)
a) d)b) e)c)
![Page 471: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/471.jpg)
![Page 472: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/472.jpg)
![Page 473: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/473.jpg)
![Page 474: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/474.jpg)
13
![Page 475: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/475.jpg)
01. (UEPB-99)Sejamf eg funções reais, tais que13)(!
![Page 476: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/476.jpg)
xxf e )1(log)(3
!x xg . Então, (
![Page 477: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/477.jpg)
g S
f )(x) éigual a:a)x
3c) log (x + 1) e))1log(3
![Page 478: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/478.jpg)
x
b)xd)x2
02. (UEPB-02)Sejamf e
![Page 479: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/479.jpg)
g funções deR R emR R ,,definidas por f (x) = 3x
![Page 480: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/480.jpg)
± 4 eg (x) =ax+ b
![Page 481: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/481.jpg)
. Dizemosque a funçãog é a função inversa def se, e somente se:a)a + b =
![Page 482: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/482.jpg)
0 d)b =4ab)a:b =1 e)
![Page 483: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/483.jpg)
ab =1c)a = b03. (UEPB-06)Sejam as funções deR
![Page 484: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/484.jpg)
emR , dadas por f(x) = 2x+ 1 e g(f(x)) = 4x
![Page 485: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/485.jpg)
+ 1. Calculando o valor deg(0), teremos:a) 2 c) ± 1 e) 3 b) 1 d) ± 204. (UEPB-08)Uma função real f é ímpar se f(x) = ± f(±
![Page 486: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/486.jpg)
x) para todo x no domínio de f. Qual das funções abaixo éímpar?a) f(x) = x3
d) f(x) = 2 b) f(x) = x
![Page 487: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/487.jpg)
2
e) f(x) = x6
+ 2c) f(x) = x4
+ 105. (UEPB-08)Sendo,11)(!
![Page 488: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/488.jpg)
x xf x 1 e g(x) = 2x ± 4,o valor de
¹¹ º ¸©©ª¨¹ º ¸©ª¨
![Page 489: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/489.jpg)
212f g g f é igual a:a) 1 b) ± 8 c) ± 9 d) ± 1 e) ± 206. (UEPB-08)
![Page 490: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/490.jpg)
A função definida para x 1 por 1)(!x xf tem inversa)(
![Page 491: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/491.jpg)
1xf
; então a imagem de)(1xf
![Page 492: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/492.jpg)
será:a) {y
IR
y 0} b) {y
IR
y 1}c) {y
![Page 493: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/493.jpg)
IR
y 0}d) {y
IR
y 1}e) {y
IR
![Page 494: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/494.jpg)
y ± 1}07. (UEPB-09)Se g e f são funções definidas por 1x1xg(x)!
![Page 495: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/495.jpg)
, com x ± 1, e f(x) = x± 1
, com x 0,então g(f(x)) é igual a:a) f(g(x)) d) ± g(x) b) f(x) e) ± f(x)c) g(x)
![Page 496: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/496.jpg)
08. (UEPB-09)Uma função real f é par se f(x) = f(±x) para todo x
R. Se f(x) = x4
+ px3
![Page 497: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/497.jpg)
+ x2
+ qx for par,teremos necessariamente:a) p = q = 0 d) p + q = 1 b) p = 0 e q 0 e) p
![Page 498: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/498.jpg)
= ± qc) p 0 e q = 0FFuunnççõõeessddoo11ººggrraauu f :
![Page 499: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/499.jpg)
p,f (x) = ax + b, a{
0.(se a = 0, entãof
![Page 500: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/500.jpg)
(x) = b é chamada função cons-tante).O Gráfico def (x) = ax + b, a{
0.* se a
![Page 501: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/501.jpg)
"0, então: * se a
0, então55.(F. CARLOS CHAGAS-SP)A figura seguintereprese
![Page 502: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/502.jpg)
nta a função y = mx + t. O valor da função no ponto x =31é:a)2,8 b)2,6c)
![Page 503: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/503.jpg)
2,5d)1,8e)1,7b0yRAIZ
yb0yRAIZ
![Page 504: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/504.jpg)
y30yy±2
![Page 505: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/505.jpg)
![Page 506: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/506.jpg)
![Page 507: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/507.jpg)
![Page 508: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/508.jpg)
14
![Page 509: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/509.jpg)
56. (UNI
-R I
O)Consideremos a função inversívelf
![Page 510: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/510.jpg)
cujográfico é visto ao lado. A lei que definef ±1
é:a) y = 3x +23b) y = 2x ± 23
![Page 511: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/511.jpg)
c) y =2x3± 3d) y =3x2+ 2e) y = ± 2x ± 2357.(Puc-MG/06)
![Page 512: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/512.jpg)
O gráfico representa a variação datemperatura T, medida em graus Celsius, de uma barrade ferro em função do tempo t,
![Page 513: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/513.jpg)
medido em minutos.Com base nas informações do gráfico, pode-se estimar que a temperatura dessa barra atingiu 0° C no
![Page 514: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/514.jpg)
instantet igual a:a) 1 min 15 s c) 1 min 20 s b) 1 min 25 s d) 1 min 30 s58. (UFCE)A funçãof (
![Page 515: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/515.jpg)
x) = ax+ b é tal quef (3) = 0 ef (4)"
![Page 516: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/516.jpg)
0. Pode-se afirmar que:a)a
0 b)f é crescente em todo seu domínioc)
![Page 517: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/517.jpg)
f(0) = 3d)f é constantee)f (2)"059. (UFPB-2010)
![Page 518: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/518.jpg)
Em certa cidade litorânea, a alturamáxima (H) permitida para edifícios nas proximidadesda orla marítima
![Page 519: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/519.jpg)
é dada pela funçãoH
(d ) =m
d + n,ondem
![Page 520: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/520.jpg)
ensão constantes reais ed representa adistância, em metros, do edifício até a
![Page 521: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/521.jpg)
orla marítima.De acordo com essa norma, um edifício localizadoexatamente na orla marítima tem a altura máxima
![Page 522: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/522.jpg)
permitida de 10 metros, enquanto outro edifíciolocalizado a 500 metros da orla marítima tem a alturamáxima permitida de 60
![Page 523: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/523.jpg)
metros. Com base nessasinformações, é correto afirmar que a altura máxima permitida para um edifício que será construído
![Page 524: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/524.jpg)
a 100metros da orla marítima é de:a)18 m b) 19 m c) 20 m d) 21 m e) 22 m60. (UFPB)No gráfico abaixo, estão
![Page 525: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/525.jpg)
representadasas funções definidas por g( x)=3-xef( x)
![Page 526: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/526.jpg)
=k x+t . Os valores dek et
![Page 527: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/527.jpg)
são,respectivamente:a)21e 0 b)21
e 0c) 2 e 0d) ± 2 e 1e) 2 e 161. (UERJ)
![Page 528: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/528.jpg)
A promoção de uma mercadoria em umsupermercado está representada, no gráfico a seguir, por 6 pontos de uma
![Page 529: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/529.jpg)
mesma reta.Quem comprar 20 unidades dessa mercadoria, na promoção, pagará por unidade, em reais,
![Page 530: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/530.jpg)
oequivalente a:a) 4,50 b) 5,00 c) 5,50 d) 6,00 e) 6,5001. (UEPB-01)As funções(1)e(2)
![Page 531: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/531.jpg)
definidas por 121!x yebax y!
![Page 532: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/532.jpg)
, respectivamente, estãorepresentadas graficamente abaixo.Os valores dea
![Page 533: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/533.jpg)
ebsão, res- pectivamente:a)a= 2 eb= ± 1 b)
![Page 534: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/534.jpg)
a= 3 eb= 3c)a= ± 1 eb= 3d)a
![Page 535: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/535.jpg)
= ± 5/6 eb= 3e)a= 3 eb= ± 1243
![Page 536: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/536.jpg)
xy0x y02y=
f (x )y =
![Page 537: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/537.jpg)
g ( x )
![Page 538: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/538.jpg)
![Page 539: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/539.jpg)
![Page 540: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/540.jpg)
![Page 541: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/541.jpg)
![Page 542: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/542.jpg)
15
![Page 543: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/543.jpg)
02. (UEPB-06)A figura seguinte mostra o gráfico deuma funçãog( t )
![Page 544: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/544.jpg)
com domínio [-2, 1] e imagem [0, 2],então o gráfico deg( -t )será dado por:03. (UEPB-04)
![Page 545: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/545.jpg)
Em um telefone residencial, a contamensal para as ligações é dada pela funçãoy=
![Page 546: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/546.jpg)
ax+ b,ondexé o número de chamadas mensais, com duraçãomáxim
![Page 547: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/547.jpg)
a de 3 minutos, eyé o total a ser pago em reais. No mês de abril houve 100 chamadas e a conta mensalfoi
![Page 548: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/548.jpg)
de 170 reais. Já no mês de maio houve 120chamadas e a conta mensal foi de 198 reais. Qual ototal a ser pago no mês
![Page 549: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/549.jpg)
com 180 chamadas?a) R$ 320,00 d) R$ 251,00 b) R$ 288,00 e) R$ 305,00c) R$ 222,00
![Page 550: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/550.jpg)
FFuunnççõõeessddoo22ººggrraauu Sejaf :
![Page 551: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/551.jpg)
ptal quef (x) = ax2
+ bx + c, (a{
0)O gráfico def
![Page 552: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/552.jpg)
(x) = ax2
+ bx + c, a{
0.* se(
"0, então:* se(
![Page 553: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/553.jpg)
= 0, então:* se(
0, então:Sabemos queV
![Page 554: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/554.jpg)
é o vértice da parábola e suascoordenadas são V¹ º ¸©ª¨(
aab4,2
![Page 555: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/555.jpg)
.ySe a"0, então o vérticeVé ponto de mínimo.
![Page 556: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/556.jpg)
ySe a
0, então o vérticeVé ponto de máximo.62.
![Page 557: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/557.jpg)
(UFAC)Um gráfico que pode representar a funçãof : IR pIR , x
![Page 558: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/558.jpg)
pf (x) = ax2
+ bx + c,em que a, b, c
IR, e valem as condições b2
![Page 559: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/559.jpg)
± 4ac"0, 2a"0 e ac"0,é dado pela figura:a) b)x2
![Page 560: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/560.jpg)
x1yycyV0x2
![Page 561: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/561.jpg)
x1yyycyV0y
![Page 562: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/562.jpg)
cV0ycyV0yc
![Page 563: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/563.jpg)
V0cV0
![Page 564: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/564.jpg)
![Page 565: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/565.jpg)
![Page 566: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/566.jpg)
![Page 567: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/567.jpg)
![Page 568: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/568.jpg)
![Page 569: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/569.jpg)
![Page 570: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/570.jpg)
![Page 571: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/571.jpg)
![Page 572: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/572.jpg)
![Page 573: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/573.jpg)
16
![Page 574: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/574.jpg)
y =f y =g
4 ABxyc) d)
![Page 575: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/575.jpg)
63.(UFPB)Um míssil foi lançado acidentalmente do pontaA, como mostra a figura abaixo,
![Page 576: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/576.jpg)
tendo comotrajetória o gráfico da funçãof (x) = ± x2
+ 70x onde xé dado em km.
![Page 577: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/577.jpg)
Desejando-se destruí-lo num pontoB,que está a uma distância horizontal de 40 km deA
![Page 578: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/578.jpg)
,utiliza-se um outromíssil que se movi-menta numa trajetóriadescrita, segundo ográfico da funçãog
![Page 579: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/579.jpg)
(x) =k x. Então, paraque ocorra a destruí-ção no ponto determi-nado, deve-se tomar k
![Page 580: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/580.jpg)
igual a:a) 20 b) 30 c) 40 d) 50 e) 6064. (UFPB)A função C(x) = 2x2
± 400x + 10.000represen
![Page 581: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/581.jpg)
ta o custo de produção de uma empresa para produzir xunidades de um determinado produto, por mês. Para que o
![Page 582: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/582.jpg)
custo seja mínimo, o valor dexserá:a) 400 b) 300 c) 200 d) 100 e) 5065. (UFPB-06)
![Page 583: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/583.jpg)
O gráfico da funçãox x ) x( f y5120012
!!
![Page 584: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/584.jpg)
, representado na figuraabaixo, descreve a trajetória de um projétil, lançado a partir da
![Page 585: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/585.jpg)
origem.Sabendo-se quexeysão dados em quilômetros, aaltura máximaH
![Page 586: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/586.jpg)
e o alcanceAdo projétil são,respectivamente,a) 2k m
e 40k m
![Page 587: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/587.jpg)
. d) 10k m
e 2k m
. b) 40k m
e 2k
![Page 588: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/588.jpg)
m
. e) 2k m
e 20k m
.c) 2k m
e 10
![Page 589: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/589.jpg)
k m
.66. (UFPB±99)Considere a função? Ap
7,1:
![Page 590: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/590.jpg)
f R definida por 86)(2
!x x xf . Sejam
![Page 591: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/591.jpg)
meM ,respectivamente, o menor e o maior valor que)(x
![Page 592: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/592.jpg)
f pode assumir. Amédia aritméticaentremeM
![Page 593: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/593.jpg)
é iguala) 6 b) 12 c) 7 d) 9 e) 867. (UFSC)Assinale a ÚNICA proposição COR-RETA.A figura a seguir representa o
![Page 594: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/594.jpg)
gráfico de uma parábolacujo vértice é o ponto V. A equação da reta r é:a) y = ± 2x + 2 d) y = 2x + 2 b) y = x + 2 e) y
![Page 595: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/595.jpg)
= ±2x ± 2c) y = 2x + 168. (UFPB-07)A função27
0012
00100 )( 2
!
x x x L
![Page 596: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/596.jpg)
representa o lucro deuma empresa, em milhões de reais, ondexé aquantidade de unidades vendidas.
![Page 597: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/597.jpg)
Nesse contexto,considere as seguintes afirmações:I. Se vender apenas 2 unidades, a empresa terá lucro.II. Se
![Page 598: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/598.jpg)
vender exatamente 6 unidades, a empresa terálucro máximo.III. Se vender 15 unidades, a empresa terá
![Page 599: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/599.jpg)
prejuízo.Está(ão) correta(s) apenas:a) I d) I e II b) II e) II e IIIc) III69.(UFPB-04)
![Page 600: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/600.jpg)
A figura abaixo ilustra uma pontesuspensa por estruturas metálicas em forma de arcode parábola.
![Page 601: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/601.jpg)
![Page 602: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/602.jpg)
![Page 603: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/603.jpg)
17
![Page 604: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/604.jpg)
ABD0f (x)g
![Page 605: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/605.jpg)
(x)xyOs pontosA
,B
,
![Page 606: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/606.jpg)
C
,D
eE
estão no mesmo nívelda estrada e a distância entre quaisquer
![Page 607: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/607.jpg)
doisconsecutivos é25m
. Sabendo-se que os elementosde sustentação são todos
![Page 608: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/608.jpg)
perpendiculares ao planoda estrada e que a altura do elemento centralCGé2
![Page 609: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/609.jpg)
0m
, a altura deDH
é:a)17
,5m
d)1
![Page 610: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/610.jpg)
0,0m
b)1
5,0m
e)
![Page 611: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/611.jpg)
7
,5m
c)1
2,5m
![Page 612: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/612.jpg)
70. (CEFET-06)De uma folha de cartolina com formatriangular, corta-se um retângulo como mostra na linha
![Page 613: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/613.jpg)
pontilhada da figura abaixo. Considerando-se que aárea desse retângulo deve ser máxima possível, tem-seque o valor
![Page 614: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/614.jpg)
do seu perímetro mede:a) 18 cm b) 16 cmc) 14 cmd) 12 cme) 9 cm71. (CEFET-05)
![Page 615: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/615.jpg)
Na figura abaixo estão representadosdois montes através de dois gráficos das funçõesf (
![Page 616: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/616.jpg)
x) = ± x2
± 6x ± 5 eg (x) = ± x
![Page 617: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/617.jpg)
2
+ 10x ± 16 para yu0,como mostrado. Com o objetivo de dimensionar umcabo de aço
![Page 618: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/618.jpg)
para um teleférico, deseja-se calcular adistância D entre os pontos A e B que corresponde
![Page 619: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/619.jpg)
maos extremos das funçõesf (x) eg (x
![Page 620: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/620.jpg)
), respectivamente. Nestas condições, o quadrado da distância procurada éigual a:a) 79
![Page 621: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/621.jpg)
b) 49c) 59d) 39e) 8972. (UFPB-2010)Para acompanhar o nível da água (H
![Page 622: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/622.jpg)
)do reservatório que abastece certa cidade, foram feitasmedições desse nível em um período de 12 dias,
![Page 623: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/623.jpg)
comapenas uma medição em cada dia. Após essasmedições, constatou-se que esse nível, medido emmetros,
![Page 624: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/624.jpg)
podia ser calculado por meio da funçãoH
(t ) =161
![Page 625: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/625.jpg)
t 2
+t + 3, ondet é o número de diasdecorridos a partir do
![Page 626: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/626.jpg)
início do período de observação.Com base nessas informações, identifique asafirmativas corretas:I)
![Page 627: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/627.jpg)
O nível máximo atingido pelo reservatório, aolongo do período de observação, foi de 7 metros.II)
![Page 628: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/628.jpg)
O nível da água do reservatório, final do períodode observação, era de 6 metros.III)O nível da água do reservatório, durante
![Page 629: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/629.jpg)
osúltimos quatro dias do período de observação, foisempre decrescente.IV)O nível da água do reservatório, durante os
![Page 630: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/630.jpg)
primeiros dez dias do período de observação, foisempre crescente.V)O nível da água do reservatório, no quarto dia do período de
![Page 631: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/631.jpg)
observação, foi o mesmo do ultimodia.73. (UFPB)O conjunto solução da inequação (x± 1)
![Page 632: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/632.jpg)
(± x + 2)
(x ± 3)u0 é igual a:a)[1, 2][3, +g
![Page 633: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/633.jpg)
[ d) ]± g
, 1]]2, 3[ b)]± g
, 1[[2, 3] e) ]±
![Page 634: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/634.jpg)
g
, 1][2, 3]c)]2, 3[74.(Osec-SP)
![Page 635: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/635.jpg)
Dada a inequação (x ± 2)7
(x ± 10)4
(x +5)3
![Page 636: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/636.jpg)
0, o conjunto solução é:a) {x
IR ¹x
± 5} d){x
![Page 637: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/637.jpg)
IR ¹± 5
x
10} b) {x
IR
![Page 638: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/638.jpg)
¹2
x
10} e)
c) {x
IR
![Page 639: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/639.jpg)
¹± 5
x
2}75.(PUC-CAMP)
![Page 640: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/640.jpg)
Considere as funções reais, dadas por f (x) = x,g (x) = x2
± 2x e
![Page 641: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/641.jpg)
h(x) =f (x)g (x). A funçãohtem valores positivos para
![Page 642: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/642.jpg)
todos os valores de x taisque:a) x"0 d) 0
x
2 b) x
![Page 643: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/643.jpg)
"2 e) ± 2
x
0c) x
076.
![Page 644: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/644.jpg)
(UFPB)O conjunto de todos os números reais quesatisfazem a inequação0121222u
![Page 645: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/645.jpg)
x x x x
é:a)2d) IR ± 2b) IR ± {± 1} e) IR c) IR ± {± 1, 1}10 cm
![Page 646: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/646.jpg)
8 cm
![Page 647: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/647.jpg)
![Page 648: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/648.jpg)
![Page 649: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/649.jpg)
18
![Page 650: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/650.jpg)
01. (UEPB-01)A representação gráfica do trinômioy = ax2
+ bx + c é a parábola abaixo:Assinale
![Page 651: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/651.jpg)
a alternativa correta:a) a > 0, b > 0 e c < 0 b) a < 0, b < 0 e c < 0c) a < 0, b > 0 e c > 0d) a < 0, b < 0 e c > 0e) a < 0, b > 0 e c < 0
![Page 652: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/652.jpg)
02. (UEPB-08)Sabendo que o gráfico de f(x) = ax2
+ bx+ 1 tangencia o eixo OX em um único ponto, x
![Page 653: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/653.jpg)
0
= 3, ovalor de a + b é igual a:a)92d)31b)
![Page 654: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/654.jpg)
279e)271c)95
![Page 655: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/655.jpg)
03. (UEPB-06) 06.Um setor de uma metalúrgica produzuma quantidade N de peças dada pela função N(
![Page 656: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/656.jpg)
x) =x²+ 10x,xhoras após iniciar suas
![Page 657: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/657.jpg)
atividades diárias.Iniciando suas atividades às 6 horas, o número de peças produzidas no intervalo de
![Page 658: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/658.jpg)
tempo entre as 7 e as 9horas, será igual a:a) 39 c) 25 e) 28 b) 50 d) 1604. (UEPB-02)Num jogo de futebol o goleiro repõe a
![Page 659: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/659.jpg)
bola em jogo com um balão que descreve umatrajetória curva de equaçãox x y532
![Page 660: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/660.jpg)
!. Sexeysão expressos em metros, a distância linear
![Page 661: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/661.jpg)
percorrida pela bola, medida do local do chute até o ponto ondeela toca o solo é:a) 20 metros d) 25 metros b) 10 metros e) 30
![Page 662: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/662.jpg)
metrosc) 15 metros05. (UEPB-06) 16.Um jogador chuta uma bola quedescreve no espaço uma parábola dada
![Page 663: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/663.jpg)
pela equação:y = ±3t2
+ 150t ± 288. Dizemos que a bola atinge o ponto mais alto de sua trajetória quando
![Page 664: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/664.jpg)
tfor igual a:a) 35 c) 30 e) 40 b) 20 d) 2506. (UEPB-01)Uma bola chutada de um ponto B atingeo
![Page 665: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/665.jpg)
travessão no ponto T que dista 2m
do solo. Se aequação da trajetória da bola em relação ao sistema
![Page 666: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/666.jpg)
decoordenadas indicado pela fórmula y =ax2
+ (1 ± 2a
![Page 667: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/667.jpg)
)x, então a altura máxima atingida pela bola é:a) 2,5 b) 2,25c) 2d) 3e) 2,7507. (UEPB-03)A temperatura em um
![Page 668: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/668.jpg)
frigorífico, emgraus centígrados, é regulada em função do temt, deacordo com a seguinte leif
![Page 669: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/669.jpg)
dada por 1042)(2!
t t t f , com tu0. Nessas circuns-
![Page 670: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/670.jpg)
tâncias:a) a temperatura é positiva só para 0 < t < 5. b) o frigorífico nunca atinge 0º.c) a temperatura é sempre
![Page 671: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/671.jpg)
positiva.d) a temperatura atinge o pico para t = 2.e) a temperatura máxima é 18º.08. (UEPB-04)Um foguete pirotécnico é
![Page 672: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/672.jpg)
lançado paracima verticalmente e descreve uma curva dada pelaequaçãoh= ± 40t
![Page 673: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/673.jpg)
2
+ 200t , ondehé a altura, emmetros, atingida pelo foguete emt
![Page 674: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/674.jpg)
segundos, após olançamento. A altura máxima atingida e o tempo queesse foguete permanece no ar são
![Page 675: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/675.jpg)
respectivamente:a) 250m
e 2,5s d) 150m
e 2s b) 300m
e 6s e) 100m
e 3sc) 250
![Page 676: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/676.jpg)
m
e 0s09. (UEPB-06)Um fazendeiro dispõe de um rolo dearame com 2000 m de comprimento e quer construir
![Page 677: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/677.jpg)
uma cerca com 5 fios de arame de forma retangular,aproveitando um muro existente. Dessa forma, a áreamáxima
![Page 678: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/678.jpg)
obtida será:a) 20000 m2
c) 18750 m2
e) 22000 m2
b) 15000 m2
d) 16800 m
![Page 679: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/679.jpg)
2
10. (UEPB-04)O conjunto de todos os valores reais dexque satisfazem a desigualdade045
![Page 680: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/680.jpg)
2
uxé:a) {x
R R /x"2} b) {x
![Page 681: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/681.jpg)
R R /x
± 2 oux"2}c) {x
R R /
![Page 682: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/682.jpg)
x{
2}
![Page 683: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/683.jpg)
![Page 684: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/684.jpg)
![Page 685: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/685.jpg)
![Page 686: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/686.jpg)
191 2-2d) {x
R R / ± 2x
2}e) vazio11. (UEPB-09)
![Page 687: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/687.jpg)
Seja a função f(x) = x2
± 4x +c,cconstante real. Qual das
![Page 688: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/688.jpg)
alternativas abaixo é averdadeira?a) O gráfico de f ± 1
(x) é uma parábola com eixo paralelo ao eixo y. b) Se
![Page 689: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/689.jpg)
x 0, f é injetivac) A função f(x) admite inversa f ± 1
(x) para todo x reald) Se x
![Page 690: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/690.jpg)
2, f admite inversa f ± 1
(x)e) Sec> 4, o gráfico de f ± 1
corta o eixo y.
![Page 691: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/691.jpg)
12. (UEPB-09)O conjunto-solução da inequação065x65x22u
x x
![Page 692: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/692.jpg)
é igual a:a) S = {x
R / x < ± 3 ou ± 2 x 2 ou x > 3} b) S = {x
![Page 693: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/693.jpg)
R / x < ± 3 ou ± 2
x 2 ou x > 3}c) S = {x
R / x < ± 3 ou ± 2
![Page 694: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/694.jpg)
x
2 ou x 3}d) S = {x
R / x < ± 3 ou ± 2
![Page 695: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/695.jpg)
x 2 ou x 3}e) S = {x
R / x < ± 3 ou ± 2 x 2 ou x 3}FFuunnççããoo
![Page 696: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/696.jpg)
MMoodduullaarr O Módulo de um Número RealSendo x um número real, indicamos omó
![Page 697: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/697.jpg)
dulode x (ouvalor absolutode x) por ±x¹que é definido da
![Page 698: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/698.jpg)
seguintemaneira:±x¹= x, se xu0 ou
![Page 699: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/699.jpg)
±x¹= ± x, se xe
0Tem-se:1)!2x
![Page 700: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/700.jpg)
±x¹, para todo x
IR.2) Sendo a um número real tal que a"
![Page 701: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/701.jpg)
0, então:a)±x¹= a
x = a ou x = ± a b)±
![Page 702: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/702.jpg)
x¹"a
x"a ou x
![Page 703: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/703.jpg)
± ac)±x¹
a
± a
![Page 704: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/704.jpg)
x
a3) Sejaf : IR pIR, a função definida por f
![Page 705: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/705.jpg)
(x) =x,tal que:°¯®u!
![Page 706: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/706.jpg)
0se,0se,)(x x x x xf Observe o gráfico da funçãof : IR p
![Page 707: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/707.jpg)
IR, definida por f (x) =x.f
![Page 708: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/708.jpg)
(±2) =¬±2¹= 2f (±1) =¬±1
![Page 709: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/709.jpg)
¹= 1f (0) =¬0¹= 0f
![Page 710: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/710.jpg)
(1) =¬1¹= 1f (2) =¬2
![Page 711: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/711.jpg)
¹= 2A funçãof (x) =x
![Page 712: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/712.jpg)
é definida por duas sentenças:Paraxu0pf (
![Page 713: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/713.jpg)
x) =xParax
0pf
![Page 714: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/714.jpg)
(x) = ± x77.(UFPB-04)Para todosy x
![Page 715: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/715.jpg)
,IR, é verdade quea)
xyxy2!
b)||||||||
![Page 716: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/716.jpg)
yxyx!
c)||||yxyx22!
d)
||||
![Page 717: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/717.jpg)
yxyx2!
e)
||yxyx2!
78.
![Page 718: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/718.jpg)
(PUC-MG)O conjuntoS
das soluções da equação¬2x ± 1¹= x ± 1 é:a)
![Page 719: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/719.jpg)
S
=À¿¾°
¦
32,0d)S
= {0, ± 1} b)S
=
![Page 720: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/720.jpg)
e)S
=À¿¾°
§
54,0c)S
=
![Page 721: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/721.jpg)
À¿¾°¯
31,079. (FEI
-SP)O produto das raízes da equação
![Page 722: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/722.jpg)
x x x!21é:a) 1 b) ± 1 c) 2 d) ± 2 e) 080. (UEL-PR)Seja
![Page 723: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/723.jpg)
po produto doas soluções reais daequação221!x. Então
![Page 724: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/724.jpg)
pé tal que:a) p
± 4 d) 0
p
4 b) ± 2
p
![Page 725: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/725.jpg)
0 e) p"16c) 4
p
16
![Page 726: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/726.jpg)
![Page 727: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/727.jpg)
![Page 728: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/728.jpg)
20
![Page 729: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/729.jpg)
±1 110xy
81.A solução da equação53!
![Page 730: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/730.jpg)
x xé igual a:a) {± 1, 4} c) {± 1} e) {4} b) {± 1, 3, 4} d) {3, 4}82. (UFPB)Sejamf (x) =
![Page 731: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/731.jpg)
7
xe g(x) =x+ 5. Oconjunto solução da inequação (f S
![Page 732: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/732.jpg)
g)(x)u1 é:a) {x
R; 1e
xe
2} d) {x
![Page 733: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/733.jpg)
R; xe
0} b) {x
R; xu2} e) {x
R; xe
![Page 734: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/734.jpg)
0 ou xu1}c) {x
R; xe
1 ou xu3}
![Page 735: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/735.jpg)
83. (PUC-MG)O conjunto solução de 3
12xe
5 emIR é dado por:a) {x
![Page 736: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/736.jpg)
R R / ± 2exe
3} b) {x
R R / ± 2exe
![Page 737: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/737.jpg)
5}c) {x
R R / ± 2ex
± 1 ou 2xe
![Page 738: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/738.jpg)
3}d) {x
R R / ± 2x
1 oux"2}e) {x
![Page 739: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/739.jpg)
R R /x
± 1 ou 2xe
3}84. (UECE)
![Page 740: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/740.jpg)
Dados os conjuntosA = {x
>/5x
![Page 741: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/741.jpg)
3} eB = {x
>/4x
u
![Page 742: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/742.jpg)
1}, a soma dos elementos deA
B é igual a:a) 19 b) 20 c) 21 d) 22 e) 2385. (UEMS)
![Page 743: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/743.jpg)
O gráfico que representa a função y=¬x ± 2¹é:a) d) b) e)c)86. (PUC-RS)
![Page 744: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/744.jpg)
O gráfico que representa a funçãof : IR pIR definida por 1)(!
![Page 745: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/745.jpg)
x xf é:a) d) b) e)c)87. (CEFET-05)A funçãof : IR p
![Page 746: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/746.jpg)
IR correspondenteao gráfico mostrado abaixo é dado por:a)f (x
![Page 747: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/747.jpg)
) =x+ 1 b)f (x) =1
![Page 748: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/748.jpg)
xc)f (x) = 1 ± xd)f
![Page 749: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/749.jpg)
(x) =1xe)f (
![Page 750: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/750.jpg)
x) =1x01. (UEPB-02)Seae
![Page 751: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/751.jpg)
bsão dois números reais positivostal quea<b
![Page 752: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/752.jpg)
, então podemos dizer que a equação©x ± a¼=b
![Page 753: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/753.jpg)
tem:a) uma raiz positiva e outra nula. b) uma raiz positiva e outra negativa.c) duas raízes negativas.d) duas raízes
![Page 754: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/754.jpg)
positivas.e) uma única solução.02. (UEPB-03)Dadas as sentenças:I
.
![Page 755: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/755.jpg)
22222!
2240
![Page 756: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/756.jpg)
2±20±22240±2
![Page 757: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/757.jpg)
2130±2204±2
![Page 758: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/758.jpg)
± 11 ± 11 ± 1± 1± 11
![Page 759: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/759.jpg)
![Page 760: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/760.jpg)
![Page 761: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/761.jpg)
![Page 762: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/762.jpg)
![Page 763: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/763.jpg)
2
±3 ±2 ±1 0 1 2 3248xy±3 ±2 ±1 0 1 2 3248xyx
![Page 764: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/764.jpg)
yax
x11
axx22
a
![Page 765: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/765.jpg)
xxyax
x11
axx2
![Page 766: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/766.jpg)
2
axII
.1112!
x x xpara todox
![Page 767: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/767.jpg)
real.III
.11!
x xpara todoxu
![Page 768: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/768.jpg)
1.Assinale a alternativa correta:a) Somente aII
é falsa. b) Todas são verdadeiras.c) Somente a
![Page 769: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/769.jpg)
III
é verdadeira.d) Todas são falsas.e) Somente aI
é verdadeira.03. (UEPB-08)A solução de
![Page 770: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/770.jpg)
©x + 1¹= 3x + 2 é dado por:a) S = { } d) S =À¿¾°¯®
![Page 771: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/771.jpg)
43,21b) S =À¿¾°¯®32e) S =À¿¾°¯®
![Page 772: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/772.jpg)
21c) S =À¿¾°¯®43EEqquuaaççãã
![Page 773: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/773.jpg)
ooEExxppoonneenncciiaall Equação exponencial é uma equação em que aincógnita
![Page 774: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/774.jpg)
apresenta-se no expoente da potência.A resolução de uma equação exponencial baseia-se emdois casos importantes:1º)
![Page 775: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/775.jpg)
transformar a equação em igualdade de potênciasde mesma base.Ex: 2x+ 1
= 32
![Page 776: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/776.jpg)
2x+ 1
= 25x+ 1= 5x
![Page 777: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/777.jpg)
= 42º) as equações exigem transformações e artifícios.Ex: 22x
± 5
![Page 778: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/778.jpg)
2x
+ 4 = 0
(2x
)2
± 5
2
![Page 779: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/779.jpg)
x
+ 4 = 0, substituir 2x
= y
y2
± 5y + 4 = 0(
![Page 780: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/780.jpg)
= 25 ± 16 = 9y =°¯®!!
s
1y4y235, como 2x
= y, temos:y
![Page 781: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/781.jpg)
2x
= 4
2x
= 22x= 2
![Page 782: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/782.jpg)
y2x
= 1
2x
= 20x
![Page 783: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/783.jpg)
= 0S
= {0, 2}FFuunnççããooEExxppoonneenncciiaallToda funçãof
![Page 784: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/784.jpg)
: IR pIR, definida por f (x) =a
![Page 785: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/785.jpg)
x
, sendoapositivo e diferente de 1 é uma função exponencial.Toda funçãof
![Page 786: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/786.jpg)
: IR pIR,f (x) =ax
![Page 787: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/787.jpg)
, coma"1 écrescente e sua imagem éf (x)
![Page 788: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/788.jpg)
"0.Ex:f (x) = 2xx Y
![Page 789: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/789.jpg)
±3 1/8 ±2 1/4 ±1 1/20 11 22 43 8Toda funçãof : IR pIR,f (
![Page 790: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/790.jpg)
x) =ax
, com 0a
1 édecrescente e sua imagem é
![Page 791: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/791.jpg)
f (x)"0.Ex:f (
![Page 792: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/792.jpg)
x) =x
¹ º ¸©ª¨21x Y
±3 8 ±2 4 ±1 20 11 1/22 1/43 1/8II
![Page 793: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/793.jpg)
nneeqquuaaççããooEExxppoonneenncciiaallNa resolução de inequações exponenciais,
![Page 794: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/794.jpg)
devemostransformar as potências à mesma base e interpretar osentido das desigualdades conforme os
![Page 795: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/795.jpg)
gráficos dasfunçõesf (x) = ax
.1º caso: a
![Page 796: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/796.jpg)
"1 2º caso: 0
a
11212
aax x
![Page 797: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/797.jpg)
x x
""1212
aax xx x
"
![Page 798: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/798.jpg)
O sentido da desigualdade O sentido da desigualdadese conserva. se inverte.
![Page 799: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/799.jpg)
![Page 800: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/800.jpg)
![Page 801: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/801.jpg)
![Page 802: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/802.jpg)
![Page 803: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/803.jpg)
![Page 804: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/804.jpg)
22
![Page 805: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/805.jpg)
xyx1
x2
11a
logx2a
log
![Page 806: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/806.jpg)
xxa
logxyx1
x2
11a
![Page 807: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/807.jpg)
logx2a
logxxa
loga"
![Page 808: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/808.jpg)
1xx1
x2
11a
logx2a
logx
![Page 809: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/809.jpg)
xa
log1a2a12
loglogx x x x
" "LLooggaarriittmmoo
![Page 810: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/810.jpg)
Dados os números reaisaeb, ambos positivos comb{
![Page 811: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/811.jpg)
1, existe sempre um único realxtal quebx
=a. Oexpoente
![Page 812: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/812.jpg)
x, que deve ser colocado na basebpara que oresultado sejaa
![Page 813: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/813.jpg)
, recebe o nome delog ar i
t m
ode
![Page 814: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/814.jpg)
ana baseb, ou seja:±°±
©
!{""!!
![Page 815: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/815.jpg)
aabxaxx b
b1 b0, b0ater se-deveisso para,log
![Page 816: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/816.jpg)
Propriedades dos logaritmosSatisfeitas as condições de existência dos logaritmos,tem-se:* Conseqüência da definição:
![Page 817: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/817.jpg)
abab!log
*1log!bb
*01log
![Page 818: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/818.jpg)
!c
*N M N M bbb
loglog)(log!
*N M N M bbb
![Page 819: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/819.jpg)
logloglog!¹ º ¸©ª¨*
M k M bk
b
![Page 820: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/820.jpg)
loglog!
*baaccb
logloglog!
*M M aa
![Page 821: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/821.jpg)
logcolog!
EEqquuaaççõõeessLLooggaarrí í ttmmiiccaass
![Page 822: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/822.jpg)
Equação logarítmica é uma equação na qual a inço-gnita é logaritmando e/ou base de um logaritmo indicado.A
![Page 823: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/823.jpg)
resolução de uma equação logarítmica é efetuadaaplicando ou voltando as propriedades operatórias delogaritmos e analisando a
![Page 824: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/824.jpg)
condição de existência doslogaritmos indicados.Ex: Resolver a equação 3)1(log)1(log22!
![Page 825: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/825.jpg)
x xResolução:primeiro, devemos estudar a condição deexistência.
![Page 826: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/826.jpg)
x+ 1"0px"± 1x
![Page 827: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/827.jpg)
± 1"0px"1Para a sua resolução, vamos voltar à
![Page 828: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/828.jpg)
propriedade dologaritmo do produto.3)1(log)1(log22
!x x
3)1()1(log
![Page 829: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/829.jpg)
2
!
x x
3)1(log22!
x
![Page 830: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/830.jpg)
x2
± 1 = 23x2
= 9x=
![Page 831: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/831.jpg)
s
3Pela condição de existência, a resposta éx= 3S
={ 3 }
![Page 832: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/832.jpg)
FFuunnççããooLLooggaarrí í ttmmiiccaa Toda funçãof : IR p
![Page 833: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/833.jpg)
IR definida por x xf a
log)(!
sendo a"0 e a{
![Page 834: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/834.jpg)
1 é uma função logarítmica.Vamos analisar os gráficos das funções logarítmicasx xf
![Page 835: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/835.jpg)
a
log)(!
, considerando a"1 ou 0
a
![Page 836: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/836.jpg)
1.1º caso: a"1Toda função logarítmicax xf a
![Page 837: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/837.jpg)
log)(!, comx"0 ea"
![Page 838: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/838.jpg)
1 é crescente e sua imagem é IR.2º caso: 0
a
1
![Page 839: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/839.jpg)
Toda função logarítmicax xf a
log)(!, comx"
![Page 840: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/840.jpg)
0 e0
a
1 é decrescente e sua imagem é IR.II
![Page 841: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/841.jpg)
nneeqquuaaççõõeessLLooggaarrí í ttmmiiccaass Na resolução de inequações logarítmicas
![Page 842: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/842.jpg)
devemostransformar os logaritmos à mesma base e interpretar osentido da desigualdade conforme os
![Page 843: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/843.jpg)
gráficos dasfunçõesx xf a
log)(!.x
![Page 844: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/844.jpg)
"1
![Page 845: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/845.jpg)
![Page 846: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/846.jpg)
![Page 847: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/847.jpg)
23
![Page 848: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/848.jpg)
0
a
1xx1
x2
1
![Page 849: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/849.jpg)
1a
logx2a
logxxa
log1a2a12
loglogx x x x
![Page 850: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/850.jpg)
"O sentido da desigualdade se inverte.88.(Fuvest)Dado o sistema±°
![Page 851: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/851.jpg)
±
!!
913982x y y x
pode-se dizer que x + y é igual a:a) 18 b)
![Page 852: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/852.jpg)
± 21 c) 27 d) 3 e) ± 989. (FESP-SP)O triplo do valor dexque satisfaz aequação343224
![Page 853: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/853.jpg)
12!x x
é:a) 2 b) 6 c) 0 d) 9 e) 390. (PUC-MG)A soma dos zeros da funçãof
![Page 854: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/854.jpg)
(x) =223211
x x
![Page 855: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/855.jpg)
é:a) 1,5 b) 2,5 c) 3,0 d) 4,0 e) 5,091. (UCDB-MS)O conjunto verdade da equaçãoexponencial
![Page 856: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/856.jpg)
1 1223213 1 3 2!x x x x
é:a)À¿¾°
![Page 857: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/857.jpg)
23 ,32d) {1, 0} b)À¿¾°
23 ,32e) {1, ± 1}c)À¿¾°
![Page 858: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/858.jpg)
23 ,3292. (UFGO)Os valores reais dexpara os quais)1(34
![Page 859: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/859.jpg)
)8,0()8,0(2
"x x x
são:a) ± 1,5
x
![Page 860: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/860.jpg)
1,5 d) ± 0,5
x
1,5 b) ± 1,5
x
0,5 e) ndac) x
![Page 861: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/861.jpg)
0,5 ou x"1,593. (FGV-SP)A solução da inequação248212
![Page 862: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/862.jpg)
e
¹ º ¸©ª¨x x
é o conjunto dosxreais tais que:a) ± 2
![Page 863: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/863.jpg)
e
xe
2 d) ± 2e
xe
± 1 b) xe
± 2 ou x
![Page 864: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/864.jpg)
u± 1 e) xe
± 1 ou xu2c) ± 1e
xe
![Page 865: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/865.jpg)
294. (UFSM-99)A figura mostra um esboço do gráfico da funçãoy = ax
+ b, com a, b
![Page 866: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/866.jpg)
IR, a"0, a{
1 e b{
0. Então, ovalor de a2
![Page 867: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/867.jpg)
± b2
éa) ±3 b) ±1 c) 0 d) 1 e) 395. (UFRN-01)No plano cartesiano abaixo, estãorepresenta
![Page 868: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/868.jpg)
dos o gráfico da funçãox
y2!
, os núme-rosa, b, c e suas imagens.Observando-se
![Page 869: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/869.jpg)
a figura, pode-se concluir que,em
f unção dea, os valores de b e c são,
![Page 870: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/870.jpg)
respectivamente:O sentido da desigualdade é conservada
![Page 871: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/871.jpg)
![Page 872: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/872.jpg)
![Page 873: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/873.jpg)
![Page 874: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/874.jpg)
![Page 875: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/875.jpg)
![Page 876: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/876.jpg)
![Page 877: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/877.jpg)
![Page 878: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/878.jpg)
24
![Page 879: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/879.jpg)
a)2ae 4a c) 2a e4ab) a ± 1 e a + 2 d) a + 1 e a ± 296. (UFPB-05)Sendoa
![Page 880: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/880.jpg)
ek
constantes reais e sabendo-seque o gráfico da funçãof (x) =a
![Page 881: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/881.jpg)
2k
x
passa pelos pontosA(0, 5) e B(1, 10), o valor da expressão 2a +k
![Page 882: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/882.jpg)
é:a) 15 b) 13 c) 11 d) 10 e) 1297. (UFPB-2010)A vigilância sanitária, em certodia,constatou que, em uma cidade 167
![Page 883: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/883.jpg)
pessoas estavaminfectadas por uma doença contagiosa. Estudosmostram que, pelas condições sanitárias e
![Page 884: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/884.jpg)
ambientaisdessa cidade, a quantidade (Q) de pessoas infectadas por essa doença pode ser
![Page 885: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/885.jpg)
estimada pela função360
39991000.167)(t
t Q
![Page 886: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/886.jpg)
!
, ondet é o tempo, em dias,contado a partir da data de constatação da doença nacidade.
![Page 887: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/887.jpg)
Nesse contexto, é correto afirmar que, 360 dias depoisque constatada a doença, o número estimado de
![Page 888: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/888.jpg)
pessoas, nessa cidade, infectadas pela doença é de:a)520 b) 500 c) 480 d) 460 e) 44098.(UESP
![Page 889: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/889.jpg)
I
)Assinalar a alternativa falsa, sobre as propriedades dos logaritmos:a) 01log
![Page 890: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/890.jpg)
!a
b)bm
bam
a
log1log)(!
![Page 891: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/891.jpg)
c)abbcac
logloglog!d)cbcbaaa
loglog)(log
![Page 892: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/892.jpg)
!e)bnbana
log)(log!
![Page 893: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/893.jpg)
99. (Unilus-SP)Ao chegar na sala de aula, Joãozinho perguntou ao professor de matemática: Qual o valor
![Page 894: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/894.jpg)
numérico da expressão x + y + z ?´. Este respondeu-lhecom certa ironia: Como queres saber o valor numéricode
![Page 895: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/895.jpg)
uma expressão, sem atribuir valores às variáveis?´.Agora, eu é que quero saber qual o valor numéricodaquela expressão
![Page 896: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/896.jpg)
quando x = 001010,log ,y =3242log
![Page 897: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/897.jpg)
e z = 12502,log . Qual deverá ser aresposta correta que Joãozinho
![Page 898: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/898.jpg)
deverá dar?a) ± 3 b) 3 c)29d)23e)23100.
![Page 899: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/899.jpg)
(UFSCar-SP)A altura média do tronco de certaespécie de árvore, que se destina à produção demadeira, evolui, desde
![Page 900: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/900.jpg)
que é plantada, segundo oseguinte modelo matemático:h( t) = 1,5 + )1t(log3
![Page 901: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/901.jpg)
,com h(t) em metros et em anos. Se uma dessas árvoresfoi cortada quando seu tronco atingiu 3,5 m
![Page 902: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/902.jpg)
de altura, otempo (em anos) transcorrido do momento da plantação até o do corte foi de:a) 9 b) 8 c) 5 d) 4 e) 2
![Page 903: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/903.jpg)
101. (UEL-PR)Quaisquer que sejam os números reais positivosa, b, c, d,xe
![Page 904: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/904.jpg)
y, a expressão:¹¹ º ¸©©ª¨¹ º ¸©ª¨¹ º ¸©ª¨¹ º ¸©ª¨
![Page 905: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/905.jpg)
d yaxd ccbba2222
loglogloglogpode ser reduzida a:a)¹ º ¸©ª¨
![Page 906: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/906.jpg)
x y2
logc) 1 e)¹¹ º ¸©©ª¨xd ya222
![Page 907: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/907.jpg)
logb)¹¹ º ¸©©ª¨y x2
logd) 0102. (Fafi-BH)O valor de
![Page 908: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/908.jpg)
? A125253
2logloglogcoé:a) 0 b) ± 1 c) 2 d) 3 e) 1103. (
![Page 909: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/909.jpg)
MACK-SP)Seam!
5l o g ebm!
![Page 910: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/910.jpg)
3l o g , 0m{
1então53log1m
é igual a:a)ab
![Page 911: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/911.jpg)
d)bab)b ± ae)a± bc) 3
![Page 912: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/912.jpg)
a± 5b104. (COVEST)Seja
5)(
![Page 913: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/913.jpg)
22log1!xexf e
![Page 914: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/914.jpg)
. Um quo-ciente das soluções da equaçãof (x) = 12x pode ser:a)65b) 5 c) 6 d)31
![Page 915: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/915.jpg)
e)56105.(UFPB-01)Sabe-se que6610,1log10!m
e que
![Page 916: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/916.jpg)
6610,3log160!m
, m{
1. Assim o valor de mcorrespondente
![Page 917: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/917.jpg)
a:a) 4 b) 2 c) 9 d) 3 e) 5
![Page 918: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/918.jpg)
![Page 919: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/919.jpg)
![Page 920: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/920.jpg)
![Page 921: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/921.jpg)
![Page 922: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/922.jpg)
25
![Page 923: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/923.jpg)
106. (UF-AL)A expressão N(t) = 1500
20,2t
permite ocálculo do número de
![Page 924: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/924.jpg)
bactérias existentes em umacultura, ao completar thoras do início de suaobservação (t = 0). Após
![Page 925: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/925.jpg)
quantas horas da primeiraobservação terá 250.000 bactérias nessa cultura?Dados: log 2 = 0,30 e log 3 = 0,48a)
![Page 926: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/926.jpg)
37 b) 35 c) 30 d) 27 e) 25107. (UFCE)Sea!
875log7
, então 245log35
![Page 927: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/927.jpg)
é iguala)72aad)27aab)
![Page 928: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/928.jpg)
52aae)75aac)25
![Page 929: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/929.jpg)
aa108.(UFMG)Observe a figura abaixo. Nessa figura estárepresentad
![Page 930: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/930.jpg)
o o gráfico da funçãobax xf !
1log)(2
.Então,f
![Page 931: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/931.jpg)
(1) é igual a:a)± 3 b)± 2c)± 1d)21
e)31
![Page 932: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/932.jpg)
109. (UFPB-04)Sabendo-se que, neste século, onúmero de habitantes de uma
![Page 933: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/933.jpg)
determinada cidade,no anox, é estimado pela função10002102000-xlog5000h(x)¹ º ¸©ª¨
![Page 934: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/934.jpg)
!,pode-se firmar que o número estimado de habitantes dessa cidade, noano de2
![Page 935: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/935.jpg)
030, estará entrea) 4000 e 5000 d) 7000 e 8000 b) 5000 e 6000 e) 8000 e 9000c) 6000 e 7000
![Page 936: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/936.jpg)
110. (UFPB-08)O percurso de um carro, em umdeterminado rali, está representado na figura a seguir,onde os
![Page 937: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/937.jpg)
pontos de partidaA¹ º ¸©ª¨12
1y ,e chegada
![Page 938: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/938.jpg)
C (16,y2) pertencem ao gráfico da funçãox log )x ( f 2
!
![Page 939: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/939.jpg)
. O carro fez o percurso descrito pela poligonalABC
, sendo os segmentos de retaAB
![Page 940: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/940.jpg)
eBC
paralelos aos eixosO
x eO
y
![Page 941: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/941.jpg)
, respectivamente.Considerando-se que as distâncias são medidas emkm
, é correto afirmar que
![Page 942: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/942.jpg)
esse carro percorreu:a) 17k m
c) 18,5k m
e) 21k m
b) 20
![Page 943: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/943.jpg)
k m
d) 20,5k m
111. (UFPB-07)Um artista plástico pintou um painel
![Page 944: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/944.jpg)
nafachada de um prédio, que está representado,graficamente, pela parte hachurada da figura abaixo.Sabe-se
![Page 945: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/945.jpg)
que a região retangular ABC D
representa o painel. De acordo com a
![Page 946: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/946.jpg)
figura, pode-se concluir quea área do painel, emm2
, é:a)32log 16c)4log 80
![Page 947: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/947.jpg)
e)3log 80b)8log 20d)12log 20112. (UFPB-07)
![Page 948: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/948.jpg)
Sabe-se que a pressão atmosféricavaria com a altitude do lugar. Em Fortaleza, ao níveldo mar, a pressão é 760
![Page 949: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/949.jpg)
mi
lí m
etrosdem
ercúr i
o(760mmH
![Page 950: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/950.jpg)
g ). Em São Paulo, a 820m
etrosde altitude,ela cai um pouco. Já em La Paz,
![Page 951: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/951.jpg)
capital da Bolívia, a3.600m
etrosde altitude, a pressão cai para,aproximadamente, 500mmH
![Page 952: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/952.jpg)
g . Nessa cidade, o ar émais rarefeito do que em São Paulo, ou seja, aquantidade de oxigênio no ar, em La Paz, é
![Page 953: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/953.jpg)
menor queem São Paulo. (Adaptado de:<www.searadaciencia.ufc.br >. Acesso em: 02 ago.2006).
![Page 954: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/954.jpg)
x ±45yy
![Page 955: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/955.jpg)
![Page 956: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/956.jpg)
![Page 957: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/957.jpg)
2
Esses dados podem ser obtidos a partir da equação¹ º ¸©ª¨!P h 7
60l
![Page 958: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/958.jpg)
g 1840010
, que relaciona a pressãoatmosféricaP
,dada emmm
![Page 959: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/959.jpg)
H
g , com a alturah, emmetros, em relação ao nível do mar.Com base nessa equação,
![Page 960: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/960.jpg)
considere as seguintesafirmações:I. Quandoh=1840m
, a pressão seráP
![Page 961: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/961.jpg)
=76mmH
g .II. Quando P=7,6mmH
g , a altura será
![Page 962: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/962.jpg)
h=36800m
.III. A pressãoP
é dada em função da alturah
![Page 963: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/963.jpg)
pelaexpressão18400
107
60h
P
v!
.De acordo com as informações
![Page 964: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/964.jpg)
dadas, está(ão)correta(s) apenas:a) I d) I e II b) II e) II e IIIc) III113. (CEFET-05)
![Page 965: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/965.jpg)
Qual o maior valor real do conjuntosolução da equação212log9!
¹ º ¸©ª¨
x x
![Page 966: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/966.jpg)
, na variávelx?114. (UFMG)Sobre as raízes da equação
06log5log10210
![Page 967: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/967.jpg)
!x xé correto afirmar que:a)não são reais b)
![Page 968: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/968.jpg)
são números irracionaisc)são números inteiros consecutivosd)são opostase)o quociente da maior raiz pela
![Page 969: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/969.jpg)
menor raiz é igual adez.115. (Fuvest-SP)Seja f(x) =)12(log)43(log
![Page 970: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/970.jpg)
33
x xOs valores dex, para os quaisf está definida e satisfazf(x
![Page 971: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/971.jpg)
)"1, são:a)x
37d)34
![Page 972: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/972.jpg)
xb)21xe)34
![Page 973: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/973.jpg)
x
21c)21x
37116.
![Page 974: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/974.jpg)
A solução da equação 22log8log42!x x
é:a)
![Page 975: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/975.jpg)
12 b) 45 c) 10 d) 1 e) 0117. (Fuvest-SP)Seja f(x) =)12(log)43(log
![Page 976: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/976.jpg)
33
x xOs valores dex, para os quaisf está definida e satisfazf(x
![Page 977: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/977.jpg)
)"1, são:a)x
37d)34
![Page 978: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/978.jpg)
xb)21xe)34
![Page 979: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/979.jpg)
x
21c)21x
37118. (F. M.
![Page 980: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/980.jpg)
I
tajubá-MG)Resolvendo a inequaçãolog1/2
(x ± 1) ± log1/2
(x + 1) < log1/2
![Page 981: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/981.jpg)
(x ± 2) + 1encontramos:a){x
IR / 0e
xe
3} d) {x
![Page 982: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/982.jpg)
IR /2e
xe
3} b){x
IR / 0
x
![Page 983: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/983.jpg)
3} e) Nenhuma das res-c) {x
IR / 2
x
3} postas anteriores.
![Page 984: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/984.jpg)
01. (UEPB-99)Considere a equação exponencial1349121!
x x
.
![Page 985: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/985.jpg)
Com respeito a sua solução, podemos afirmar:a) a equação não possui raiz real.b) a equação admite apenas
![Page 986: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/986.jpg)
uma raiz real e essevalor real é igual a 3.c) o produto das raízes é igual a 3.d) a soma das raízes da equação é igual a 1.e) a soma
![Page 987: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/987.jpg)
das raízes da equação é igual a 0.02. (UEPB-01)A solução da equação exponencial21632!
![Page 988: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/988.jpg)
x x
é:a) um número par d) um divisor de 8 b) um número primo e) um número
![Page 989: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/989.jpg)
irracionalc) um múltiplo de dois03. (UEPB-02)A equação exponencial8191)3(2!
![Page 990: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/990.jpg)
¹ º ¸©ª¨
x x
admite duas soluções reais. Seaeb
![Page 991: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/991.jpg)
representam essa solução, então:a)a + b = ad)ab =0 b)a + b =
![Page 992: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/992.jpg)
3 e)a=bc)ab =3
![Page 993: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/993.jpg)
![Page 994: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/994.jpg)
![Page 995: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/995.jpg)
![Page 996: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/996.jpg)
![Page 997: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/997.jpg)
![Page 998: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/998.jpg)
![Page 999: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/999.jpg)
![Page 1000: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1000.jpg)
![Page 1001: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1001.jpg)
![Page 1002: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1002.jpg)
27
![Page 1003: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1003.jpg)
04.O valor dexna inequação exponencial16,025u¹ º ¸©ª¨x
![Page 1004: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1004.jpg)
é dado por:a)xu± 2 d)xe
2a)xe
± 2 a)
![Page 1005: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1005.jpg)
x<21c)xu205. (UEPB-08)
![Page 1006: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1006.jpg)
Os valores reais de x para os quais0342xex
![Page 1007: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1007.jpg)
serão:a) ± 3 < x < 3 d) x > ± 2 b) x < ± 2 ou x > 2 e) ± 2 < x < 2c) x > 206. (UEPB-07)
![Page 1008: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1008.jpg)
O conjunto solução da inequação008,0)04,0(222
"x x
![Page 1009: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1009.jpg)
é igual a:a) S = { x
R / x < 3} b) S = { x
R
![Page 1010: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1010.jpg)
/ x < ± 1 ou x > 3}c) S = { x
R / 1 < x < 3}d) S = { x
R
![Page 1011: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1011.jpg)
/ x > 1 ou x < 3}e) S = { x
R / ± 1 < x < 3}07. (UEPB-04)Na função exponencialx
![Page 1012: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1012.jpg)
xf 2)(!definida emR R, o valor def (a
![Page 1013: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1013.jpg)
)f (b) é sempre igual a:a)f (a
![Page 1014: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1014.jpg)
b) d)f (a)± f (
![Page 1015: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1015.jpg)
b) b)f (a)+f (b
![Page 1016: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1016.jpg)
) e)f (a ± b)c)f (a + b)
![Page 1017: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1017.jpg)
08. (UEPB-06)O valor de 5,0log82666,0-
é igual a:a) 4 c) 1 e) 5 b) 2 d) 309. (UEPB-06)A função f (
![Page 1018: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1018.jpg)
x) = logx
(4 ± x2
) temdomínio igual a:a) D(f) = {x
![Page 1019: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1019.jpg)
R/x> 0 ex{
1} b) D(f) = {x
![Page 1020: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1020.jpg)
R/x> 2}c) D(f) = {xR* /x
![Page 1021: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1021.jpg)
2 ex{
1}d) D(f) = {xR/ 0 <x< 2 e
![Page 1022: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1022.jpg)
x{
1}e) D(f) = {xR/ 0 <x< 2}10. (UEPB-01)
![Page 1023: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1023.jpg)
Das cinco alternativas abaixo, qual delasé sempre verdadeira?a) log a + log b = log (a + b) b) log a
![Page 1024: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1024.jpg)
b = b log ac) log ab
= b log ad) log a
log b = log (a
b)e) log a ± log b = log (a ± b)
![Page 1025: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1025.jpg)
11. (UEPB-08)Sabe-se que log10
P + log10
Q = 0,assinale a única alternativa correta:a) P
![Page 1026: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1026.jpg)
Q
0 b) P e Q são nulosc) P e Q têm sinais contráriosd) P e Q são números inteiros maiores
![Page 1027: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1027.jpg)
que 1e) P é o inverso de Q12. (UEPB-08)O valor da expressão (log3
5)
(log5
![Page 1028: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1028.jpg)
10)
(log3
10) é igual a:a) 5 b) 2 c) 3 d) 1 e) 1013.(UEPB-00)
![Page 1029: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1029.jpg)
Sabendo que8log!x
, então o valor daexpressão433logx x x x
![Page 1030: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1030.jpg)
seráa)235b)435c)335d)335
![Page 1031: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1031.jpg)
e) 3514. (UEPB-00)Uma populaçãoP
de coelhos cresce deacordo com a fórmulaP
=
![Page 1032: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1032.jpg)
600
(2,51)n
, ondenrepre-senta o tempo em anos. Dado que
![Page 1033: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1033.jpg)
log(2,51) = 0,4,serão necessários quantos anos para que essa população de coelhos atinja um total de 6 mil cabeças?a)
![Page 1034: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1034.jpg)
Dois anos e seis meses. b) Exatamente dois anos.c) Três anos e quatro meses.d) Dezesseis meses.e) Quatro anos.
![Page 1035: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1035.jpg)
15. (UEPB-07)Os átomos de um elemento químicoradioativo possuem uma tendência natural de sedesintegrarem, diminuindo,
![Page 1036: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1036.jpg)
portanto, sua quantidadeoriginal com o passar do tempo. Suponha que certaquantidade de um elemento
![Page 1037: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1037.jpg)
radioativo, com massainicial m0
(gramas), com m0
0, decomponha-seconforme o
![Page 1038: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1038.jpg)
modelo matemático m(t) = m0
1010t
, emque m(t) é a quantidade de
![Page 1039: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1039.jpg)
massa radioativa restanteno tempo t(anos). Usando a aproximação log10
2 = 0,3,
![Page 1040: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1040.jpg)
![Page 1041: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1041.jpg)
![Page 1042: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1042.jpg)
a quantidade de anos para que esse elemento sedecomponha até atingir 81
![Page 1043: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1043.jpg)
da massa inicial será:a) 60 b) 62 c) 64 d) 63 e) 7016. (UEPB-03)Na equação logarítmica21)](log[loglog324
![Page 1044: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1044.jpg)
!xo valor dexé:a) um múltiplo de 5 b) um número divisível por 3 e 9.c) um
![Page 1045: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1045.jpg)
número par.d) um número decimal.e) um número irracional.17. (UEPB-09)Os números reais positivos m, n são taisque
![Page 1046: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1046.jpg)
2log2log55!
nm. O valor de m
n é:a) 52
b) 25
![Page 1047: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1047.jpg)
c) 54
d) 53
e) 518. (UEPB-04)Em 1614, o escocês Jonh Napier (1550-
![Page 1048: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1048.jpg)
1617) criou a ferramenta de cálculo mais afiada´ que precedeu a invenção dos computadores,o log
![Page 1049: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1049.jpg)
ar i
t m
o.Sek m!
32
![Page 1050: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1050.jpg)
l o g , e n t ã o52logm
vale:a) 5k
d)5k
![Page 1051: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1051.jpg)
b)k
e)5k
c)k
+ 519. (UEPB-99)
![Page 1052: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1052.jpg)
Com respeito à inequação logarítmica)(loglog32x
0 podemos afirmar que seu
![Page 1053: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1053.jpg)
conjuntosolução é:a) {x
IR ©x{
3} d) {x
![Page 1054: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1054.jpg)
IR ©x
3} b) {x
IR ©
![Page 1055: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1055.jpg)
x"1} e)*I
Rc) {x
![Page 1056: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1056.jpg)
IR ©1x
3}20. (UEPB-09)
![Page 1057: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1057.jpg)
A solução da inequação
0105,0)1(log2
ux
![Page 1058: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1058.jpg)
é:a) 1 < x 3 d) x 2 b) 1 < x 2 e) x > 1c) 0 x 221. (UEPB)Dada a função real108332)(21
![Page 1059: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1059.jpg)
!
x xxf
O domínio dessa função érepresentado por:a) ]± g
, 2[ d) ]±
![Page 1060: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1060.jpg)
g
, 2] b) ]2, +g
[ e) IR c) [2, +g
[PPR R OOGGR R E
![Page 1061: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1061.jpg)
ESSSSÕÕEESSPPrrooggrreessssããooAArriittmmééttiiccaa
![Page 1062: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1062.jpg)
é uma sucessão de núme-ros em que cada termo, a partir do segundo, é obtido pelasoma de seu antecessor com uma
![Page 1063: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1063.jpg)
constante.Essa constante da progressão aritmética (P.A.) échamada derazão
![Page 1064: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1064.jpg)
, e é representada pela letrar .Propriedades:
![Page 1065: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1065.jpg)
* Termos eqüidistantes dos extremos(a1
, a2
, a3
, ..., a
![Page 1066: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1066.jpg)
n-2
, an-1
, an
) é PA, então:a1
+ an
= a2
![Page 1067: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1067.jpg)
+ an-1
= a3
+ an-2
= «* Média aritmética(a, b, c) é PA
![Page 1068: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1068.jpg)
2b = a + c
b =2ca
![Page 1069: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1069.jpg)
TTeerrmmooGGeerraall:: an
= a1
+ (n ± 1).r, n
2
![Page 1070: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1070.jpg)
*
SSoommaaddoossnnpprriimmeeiirroosstteerrmmoossddeeuummaaPPAA S
![Page 1071: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1071.jpg)
n
=2n)aa(n1
, n
2*
![Page 1072: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1072.jpg)
PPrrooggrreessssããoo
GGeeoommééttrriiccaa é uma sucessão de nu-meros diferentes de zero, em que cada termo, a partir dosegundo, é obtido pelo produto de seu antecedente comuma constante.Essa constante da progressão geométrica (P.G.) échamada derazão, e é representada pela letraq.Propriedade da média geométrica(a, b, c) é uma PGb2= acTTeerrmmooGGeerraall:: an= a1qn ± 1, n2*SSoommaaddoossnnpprriimmeeiirroosstteerrmmoossddaaPPGG Sn=1)1(qqan1, com q{1SSoommaaddoosstteerrmmoossddeeuummaaPPGGiinnf f iinniittaa S =q1a1
![Page 1073: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1073.jpg)
![Page 1074: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1074.jpg)
![Page 1075: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1075.jpg)
29
![Page 1076: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1076.jpg)
PPrroodduuttooddoosstteerrmmoossddeeuummaaPPGGf f iinniittaa 211q)a()-( nnnn!119. (Unifesp-SP)A soma dos termos que são números primos da seqüência cujo termo geral é dado por an= 3n + 2, parannatural, variando de 1 a 5, é:a) 10 b) 16 c) 28 d) 33 e) 36120. (Unesp-SP)Os coelhos se reproduzem maisrapidamente que as maiorias dos mamíferos. Considereuma colônia de coelhos que se inicia com um únicocasal de coelhos adultos e denote por ano número decasais adultos desta colônia ao final denmeses. Se a1=1, a2= 1 e, para nu2, an + 1= an+ an ± 1o número decasais de coelhos adultos na colônia ao final do quintomês será:a) 13 b) 8 c) 6 d) 5 e) 4121.Considere (a1, a2, a3, ..., an) uma progressãoaritmética de razão r. Então:a) ( ) a12= a18± 6r b) ( ) a28= a8+ 20r c) ( ) os termos ak + 1e an ± k são eqüidistantesdos extremos.d) ( ) para n = 51 e a1+a51
![Page 1077: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1077.jpg)
= 28, tem-se a4+ a48= 28122.(Unicap)Em uma progressão aritmética, é sabidoque a3= 5 e a9= 17. O valor de a12é:a)15 b) 17 c) 20 d) 23 e) 41123.(UFRN)Numa progressão aritmética de termo geralan, tem±se que°¯®!!1282413aaaa. O primeiro termodessa progressão é:a) 6 b) 5 c) 4 d) 3 e) 2124.(UFPB)Se o primeiro termo negativo da progressãoaritmética: 343, 336, 329, ... é an, então, o valor de n éigual a:a) 35 b) 29 c) 49 d) 50 e) 51125.SejaSa soma dos múltiplos de 7 compreendidosentre 12 e 325. A soma dos dígitos deSé igual a:a)18 b) 15 c) 21 d) 12 e) 25126.(UEL)Interpolando-se 7 termos aritméticos entre osnúmeros 10 e 98, obtém-se uma progressão aritméticacujo termo central é:a) 45 b) 52 c) 54 d) 55 e) 57127.(PUC-CAMP)Um veículo parte de uma cidade Aem direção a uma cidade B, distante 500km. Na 1ªhora do trajeto ele percorre 20km, na 2ª hora 22,5km,na 3ª hora 25km e assim sucessivamente Ao completar a 12ª hora do percurso, a distância que esse veículoestará de B é de:a)115 km d) 155 km b)125 km e) 95 kmc)135 km128. (UNICE-2000)Numa urna há 1.600 bolinhas.Retirando, sem reposição, 3 bolinhas na primeira vez,6 bolinhas na segunda, 9 bolinhas na terceira e assimsucessivamente, o número de bolinhas que restarão,após a 32ª retirada é:a)16 b) 26 c) 36 d) 46 e) 56
![Page 1078: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1078.jpg)
129.Uma bola de borracha cai de uma altura de 10metros, elevando-se em cada choque com o piso a umaaltura de 80% da altura anterior. Podemos afirmar queo comprimento percorrido pela bola até parar é:a)90 m d) 80 m b)50 m e) 70 mc)40 m130.(UFPB)Simplificando a expressão...333333x x xobtém-se:a) 1 b) 0 c)3xd)xe) 34131. (Unifor-CE)Qualquer número que pode ser representado como nas figuras abaixo é chamadonúmero triangular.yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy1 3 6 10 15Seguindo esse padrão, é correto afirmar que ovigésimo número triangular é:
![Page 1079: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1079.jpg)
![Page 1080: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1080.jpg)
![Page 1081: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1081.jpg)
![Page 1082: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1082.jpg)
![Page 1083: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1083.jpg)
![Page 1084: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1084.jpg)
![Page 1085: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1085.jpg)
![Page 1086: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1086.jpg)
30
![Page 1087: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1087.jpg)
a) 176 d) 210 b) 180 e) 240c) 196132. (UFPB-09) Em uma determinada plataformamarítima, foram extraídos 39.960barris de petróleo,em um período de 24horas. Essa extração foi feita demaneira que, na primeira hora, foram extraídosxbarris e, a partir da segunda hora,r barris a mais doque na hora anterior. Sabendo-se que, nas últimas9 h o r a s d e s s e p e r í o d o , f o r a m e x t r a í d o s 1 8 . 3 6 0 b a r r i s , o número de barris extraídos, na primeira hora, foi:a) 1180d) 1190b) 1020e) 1090c) 1065133.(UFPB)Um sargento tentou colocar 130 soldadossob seu comando, em forma de um triângulo, pondoum soldado na primeira fila, dois na segunda, três naterceira e assim por diante. No final, sobraram 10soldados. O numero de filas formadas foi de:a) 15 b) 23 c) 8 d) 10 e) 12134. (UFPB-05)Em janeiro de 2003, uma fábrica dematerial esportivo produziu 1000 pares de chuteiras.Sabendo-se que a produção de chuteiras dessa fábrica,em cada mês de 2003, foi superior à do mês anterior em 200 pares, quantos pares de chuteiras essa fábrica produziu em 2003?a) 30.000 d) 26.200 b) 25.200 e) 20.000c) 25.000135. (CEFET-05)Na apuração dos votos de umaeleição, o candidato A obteve, na primeira divulgação,512 votos e a partir daí, a cada nova divulgação, teve ototal de seus votos duplicados. Por outro lado, ocandidato B obteve, na primeira divulgação, apenas 1voto e, a partir daí, teve o total de seus votosquadruplicado a cada nova divulgação. Mantendo-seestas condições, quantas divulgações são necessárias para que se verifique um empate na eleição, contandoinclusive com a primeira divulgação?136. (UFPB-05)ParaxIR ± {0}, considere as fun-çõesf (x) =log5x,g (x) =135xeh(x) = (f Sg )(x)Se (
![Page 1088: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1088.jpg)
an) e (bn), n2± {0}, são as seqüênciasdefinidas, respectivamente, por (g (1),g (2),g (3), ... ) e(h(1),h(2),h(3), ... ) então:a) (an) é uma progressão geométrica e (bn), uma progressão aritmética. b) (an) é uma progressão aritmética e (bn), uma progressão geométrica.c) (an) e (bn) são progressões aritméticas.d) (an) e (bn) são progressões geométricas.e) Nenhuma dessas seqüências é progressão aritméticaou geométrica.137 . (UFPB-06)Uma escada foi feita com 210 blocoscúbicos iguais, que foramcolocados uns sobre osoutros, formando pilhas, demodo que a primeira pilhatinha apenas 1bloco, asegunda, 2 blocos, a terceira,3 blocos, e assimsucessivamente, até a última pilha, conforme a figura aolado.A quantidade de degraus dessa escada é:a) 50 b) 40 c) 30 d) 20 e) 10138. (UFPB-06)Socorro apaixonada por Matemática, propôs para seu filho, João: Você ganhará umaviagem de presente, no final do ano, se suas notas, emtodas as disciplinas, forem maiores ou iguais àquantidade de termos comuns nas progressõesgeométricas (1, 2, 4, ..., 4096) e (1, 4, 16, ..., 4096)´.De acordo com a proposta, João ganhará a viagem senãotiver nota inferior a:a) 6 b) 7 c) 8 d) 9 e) 10139. (UFCG-05)
![Page 1089: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1089.jpg)
Num período de 10 meses consecu-tivos, uma fábrica deseja produzir 60.000 pares decalçados, de modo que a produção a cada mês (a partir do segundo) seja 900 pares a mais, em relação ao mêsanterior. Nessas condições, a produção ao final do primeiro mês deve ser de:a)1.980 pares d) 1.850 pares b)1.890 pares e) 1.910 paresc)1.950 pares140.(UFPB)Seja (an) uma progressão geométrica cujasoma dos n primeiros termos é Sn= 3(2)n± 3 O valor do quarto termo dessa progressão é:a) 20 b) 24 c) 22 d) 17 e) 28141.Considere a seqüência (C1, C2, C3, ...) de infinitascircunferências. Se o diâmetro de C1é 80 cm e, ay
![Page 1090: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1090.jpg)
![Page 1091: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1091.jpg)
31
![Page 1092: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1092.jpg)
partir da segunda, o diâmetro de cada circunferênciaé41do diâmetro da anterior. A soma dos perímetrosdas infinitas circunferências é de:a)cm3320T d)cm3160T b)cm7150T e)T 320cmc)T 230cm142.(Unifor-CE)O número real x que satisfaz a sen-tença1 ... 8 4 2 1432!x x x xé:a) 1 b) 2 c) 3 d) 4 e) 5143. (CEFET-06)Calculando o limite da soma infinita--¹ º ¸©ª¨¹ º ¸©ª¨nn5163125691563161, ondenI2, obtemos:a) 10 b) 9 c) 8 d) 7 e) 11144.(UFPB)A soma das soluções distintas da equação322...)3(4...27494344212222!
![Page 1093: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1093.jpg)
x x x x x xnonden2, é:a) 0 b) 1 c) 2 d) ± 1 e) 401. (UEPB-99)Um agricultor pretende plantar mudas delaranja obedecendo o seguinte critério: planta-se umamuda na primeira linha, duas na segunda, três naterceira e assim sucessivamente. Assinale a alternativaque apresenta a quantidade de linhas que serãonecessárias para plantar 171 mudas de laranjas.a) 21 b) 19c) 20d) 18e) 2202. (UEPB-99)Ao dividirmos a soma...1112x x xpor ...1111753x x x xobtemos como resultado:a)x(x+ 1) d)x2(x+ 1) b)x(x± 1) e)x(x2± 1)c)x(x2+ 1)03. (UEPB-00)
![Page 1094: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1094.jpg)
Devido à sua forma triangular, o refeitóriode uma indústria tem 20 mesas na primeira fila, 24 nasegunda fila, 28 na terceira e assim sucessivamente. Sedispomos de 800 mesas, o número de fileiras de mesasnesse refeitório será de:a) 12 b) 14 c) 13 d) 16 e) 1704. (UEPB-01)Se numa progressão aritmética S10= 15 eS16= 168, então temos uma sucessão de números cujarazão r e o 1º termo a1são iguais a:a) r = ± 3 e a1= 15 d) r = 3 e a1= ± 12 b) r = 2 e a1= ± 11 e) r = ½ e a1= 14c) r = ± 2 e a1= 1305. (UEPB-02)Nos classificados de um jornal... Vendoum Corsa, ano de fabricação 97, nas seguintescondições : uma entrada de 100 reais e 36 prestaçõesmensais de valores crescentes de 200 reais, 210 reais,220 reais e assim por diante´. Nessas condições, qual ovalor da última prestação?a) 450 reais d) 500 reais b) 650 reais e) 550 reaisc) 600 reais06. (UEPB-03)Considerando quadrados de mesma área,com 4 palitos de fósforos formamos um quadrado, com7 palitos de fósforos dois quadrados, com 10 palitos defósforos 3 quadrados, ... Então com 40 palitosformamos:a) 15 quadrados d) 11 quadrados b) 13 quadrados e) 10 quadradosc) 19 quadrados07. (UEPB-04)Quantos números não divisíveis por 3existem no conjunto A = {x>/ 1exe9000}?a) 5.000 d) 6.000 b) 3.000 e) 2.000c) 4.00008. (UEPB-04)Interpolar, intercalar ou inserir mmeiosaritméticos entre os númerosaebsignifica:a) Formar uma P.A. de (m+ 2) termos entreaeb. b) Formar uma P.A. demtermos, onde o 1º termo éae o último éb.
![Page 1095: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1095.jpg)
![Page 1096: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1096.jpg)
![Page 1097: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1097.jpg)
![Page 1098: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1098.jpg)
![Page 1099: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1099.jpg)
![Page 1100: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1100.jpg)
![Page 1101: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1101.jpg)
![Page 1102: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1102.jpg)
![Page 1103: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1103.jpg)
![Page 1104: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1104.jpg)
![Page 1105: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1105.jpg)
![Page 1106: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1106.jpg)
![Page 1107: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1107.jpg)
![Page 1108: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1108.jpg)
![Page 1109: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1109.jpg)
![Page 1110: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1110.jpg)
![Page 1111: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1111.jpg)
![Page 1112: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1112.jpg)
![Page 1113: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1113.jpg)
![Page 1114: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1114.jpg)
![Page 1115: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1115.jpg)
![Page 1116: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1116.jpg)
![Page 1117: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1117.jpg)
![Page 1118: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1118.jpg)
![Page 1119: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1119.jpg)
32
![Page 1120: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1120.jpg)
c) Formar uma P.A. de (m+ 2) termos, onde o 1ºtermo éae o último éb.d) Formar uma P.A. onde todos os termos sãoeqüidistantes deaeb.e) Formar uma P.A. ande2baé a soma dosnprimeiros termos.09. (UEPB-06)Durante 160 dias consecutivos, a programação de uma TV Educativa apresentará, dentreoutras atrações, aulas deM atemát icae aulas deLiteratura, conforme indicam respectivamente as progressões (2 , 5 , 8 , ..... , 158 ) e ( 7 , 12 , 17 , ..... ,157 ), cujos termos representam as ordenações dos diasno respectivo período. Nesse caso, o número de vezes,em que haverá aula deM atemát icae aula deLiteraturano mesmo dia, é igual a:a) 14 c) 11 e) 10 b) 9 d) 1510. (UEPB-07)O Departamento Nacional de Infra-estrutura de Transporte (DNIT) quer colocar radares decontrole de velocidade, ao longo de 500 km de umarodovia. Para isto, instalou o primeiro radar no km 10, osegundo no km 50, o terceiro no km 90 e assim por diante. O número de radares que será colocado notrecho planejado é:a) 14 b) 12 c) 16 d) 13 e) 1111. (UEPB-07)Se a soma dos termos da P.G.¹¹ º ¸©©ª¨,...1,1,12x xé igual a 4, com x > 1, o valor de x éigual a:a)67b)23c)
![Page 1121: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1121.jpg)
45d)56e)3412. (UEPB-09)A soma de todos os múltiplos de 7,compreendidos entre 600 e 800, é igual a:a) 23.000 e) 20.003 b) 20.300 d) 30.002c) 20.030
![Page 1122: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1122.jpg)
![Page 1123: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1123.jpg)
![Page 1124: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1124.jpg)
![Page 1125: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1125.jpg)
![Page 1126: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1126.jpg)
![Page 1127: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1127.jpg)
![Page 1128: 1](https://reader031.fdocumentos.com/reader031/viewer/2022012403/557202484979599169a3442f/html5/thumbnails/1128.jpg)