Resoluรงรฃo โ Meta 6
A) x = 1,5
f(1,5) = -3.1,5 + 4
f(1,5) = -0,5
B) x = a + b
f(a + b) = -3.(a + b) + 4
f(a + b) = -3a - 3b + 4
QUESTรO 1.
a) Constante
b) Linear
c) Afim
d) Afim
QUESTรO 2.
f(x) = -2x + 3
a)f(1) = -2.1 + 3 = 1
b)f(0) = -2.0 + 3 = 3
c) f(๐
๐) = -2 .
๐
๐+ 3 =
๐
๐
d) f(-๐
๐) = -2.
โ๐
๐+ 3 = 4
QUESTรO 3.
a)f(x) = 1
2x + 3 = 1
x = -1
b)f(x) = 0
0 = 2x + 3
x = -3/2
QUESTรO 4.
c) f(x) = ๐
๐๐
๐= 2x + 3 (.3)
1 = 6x + 9x = -8/6
d) f(x) = 0,750,75 = 2x + 3๐
๐= 2x + 3 (.4)
3 = 8x + 12x = -9/8
QUESTรO 5.
a) f(x) = 4x + 5
Taxa de variaรงรฃo = 4
b) f(x) = 3
Taxa de variaรงรฃo = 0
QUESTรO 6.
f(x + h) โ f(x).
a) h(x) =๐
๐๐ + ๐
=๐ .(๐ + ๐)
๐+ ๐ โ (
๐
๐๐ + ๐)
=๐
๐+
๐
๐+ 3 -
๐
๐โ ๐
= ๐
๐
Afim, pois nรฃo depende de x.
b) f(x) = 2xยฒ
= 2 . (x + h) - 2xยฒ
= 2x + 2h - 2xยฒ
Nรฃo รฉ afim, pois depende de x.
QUESTรO 7.
A)
x
y
-2
-1
B)
x
y
-1
3
QUESTรO 8.
A)
x
y
0
B)
C)
x
y
5
F)
x
y
-3
D)
x
y
3
E)
x
y
0
x
y
0 -3
QUESTรO 9.
x
y
f
g
h
s
t
QUESTรO 10.
a) R: 4x + 3y + 7 = 0 e A(2,3)
d =4 . 2 + 3 . 3 + 7
๐ ๐+ ๐ ๐=๐๐
๐
b) s: 3x โ 4y + 2 = 0 e A(-1,2)
d = 3.โ1 โ 4.2 + 2
๐ ๐+ โ๐ ๐= ๐
๐
c) t: 12x + 13y + 8 = 0 e A(2, 2)
d =12.2 + 13.2 + 8
๐๐ ๐+ ๐๐ ๐=
๐๐
๐๐๐
d) z: 5x โ 4y + 8 = 0 e A(1, - 2)
d =5.1 โ 4.โ2 + 8
๐ ๐+ โ๐ ๐=
๐๐
๐๐
e) v: 3x + 4y + 8 = 0 e A(2,1)
d =3.2 + 4.1 + 8
๐ ๐+ ๐ ๐=๐๐
๐
QUESTรO 11.
a) f(x)= - 2x
Com eixo x:
โ๐
โ๐= ๐
Com eixo y:
0
b) f(x) =๐
๐๐ โ ๐
Com eixo x:
โ(โ๐)
๐๐
= ๐
Com eixo y:
-1
QUESTรO 12.
a) Afim
b) Afim
c) Constante
d) identidade
e) Linear
f) Translaรงรฃo
QUESTรO 13.
a) f(x) = 3(x+1) + 4(x โ 1)
f(x) = 3x + 3 + 4x โ 4
f(x) = 7x โ 1
a = 7 e b = -1
b) f(x) = (x+2)ยฒ + (x+2)(x-2)
f(x) = ๐๐ + ๐๐ฑ + ๐ + ๐๐ - 4
f(x) = 2๐๐ + 4x
Nรฃo รฉ funรงรฃo afim.
c) f(x) = (x-3)ยฒ - x(x-5)
f(x) = xยฒ - 6x + 9 - xยฒ + 5x
f(x) = -x + 9
a = -1 e b = 9
d) f(x) = (x-3) โ 5(x-1)
f(x) = x โ 3 โ 5x + 5
f(x) = -4x + 2
a = -4 e b = 2
QUESTรO 14.
A)
x
y5
1-3
-7
B)
x
y7
2-1
1
QUESTรO 15.
Taxa de variaรงรฃo = -3
QUESTรO 16.a) A(1, 2) e B(3, 4)
d = ๐ โ ๐ ๐ + ๐ โ ๐ ๐
d = ๐
๐ท๐ด๐ =๐+๐
๐= 2
๐ท๐ด๐ =๐+๐
๐= 3 ๐ท๐ด(๐; ๐)
b) A(-1, 0) e B(2, 7)
d = โ๐ โ ๐ ๐ + ๐ โ ๐ ๐
d = ๐๐
๐ท๐ด๐ =โ๐+๐
๐= 0,5
๐ท๐ด๐ =๐ + ๐
๐= 3,5 ๐ท๐ด(๐, ๐; ๐, ๐)
c) A(2, 9) e D(4, -5)
d = ๐ โ ๐ ๐ + ๐ โ (โ๐) ๐
d = ๐๐๐
๐ท๐ด๐ =๐ + ๐
๐= 3
๐ท๐ด๐ =๐ + (โ๐)
๐= 2 ๐ท๐ด(๐; ๐)
d) A(3, 4) e E(2, -1)
d = ๐ โ ๐ ๐ + ๐ โ (โ๐) ๐
d = ๐๐
๐ท๐ด๐ =๐ +๐
๐= 2,5
๐ท๐ด๐ =๐ + (โ๐)
๐= 1,5 ๐ท๐ด(๐, ๐; ๐, ๐)
QUESTรO 17.
a) A(2, 4) e B(6, 2)
Coeficiente Angular = โ๐ฒ
โ๐ฑ=
๐ โ ๐
๐ โ๐=
๐
โ๐= -
๐
๐
Como as retas sรฃo perpendiculares: โ๐
๐. ๐ฆ๐ฌ = โ๐
๐ฆ๐ฌ = ๐
๐ท๐ด๐ =๐+๐
๐= 4
๐ท๐ด๐ =๐ +๐
๐= 3 ๐ท๐ด(๐; ๐)
y = ax + b3 = 2.4 + bb = -5
y = 2x - 5
QUESTรO 17.
b) A(-3, 1) e B(1, 5)
Coeficiente Angular = โ๐ฒ
โ๐ฑ=
๐ โ ๐
โ๐ โ ๐=
โ๐
โ๐= 1
Como as retas sรฃo perpendiculares: 1 . ๐ฆ๐ฌ = โ๐๐ฆ๐ฌ = โ๐
๐ท๐ด๐ =โ๐ +๐
๐= -1
๐ท๐ด๐ =๐ +๐
๐= 3 ๐ท๐ด(โ๐; ๐)
y = ax + b3 = -1 . -1 + bb = 2 y = -1x + 2
QUESTรO 18.a) (r): 2x โ 3y + 7 = 0 e P(2, 3)
2x โ 3y + 7 = 0
y =2๐ฅ
3+
7
3
Como as retas sรฃo perpendiculares: 2
3. ๐ฆ๐ฌ = โ๐
๐ฆ๐ฌ =โ3
2y = ax + b
3 = โ3
2. 2 + b
b = 6
b) (r): 4x โ 3y + 1 = 0 e P(0, 0)
4x โ 3y + 1 = 0
y =๐๐
๐+
๐
๐
Como as retas sรฃo perpendiculares: ๐
๐. ๐ฆ๐ฌ = โ๐
๐ฆ๐ฌ =โ๐
๐y = ax + b
0 = โ๐
๐. ๐ + b
b = 0y = โ3๐ฑ
2+ 6 y =
โ3๐ฑ
๐
QUESTรO 18.c) (r): y = 3x โ 2 e P(3, -3)
Como as retas sรฃo perpendiculares: 3 . ๐ฆ๐ฌ = โ๐
๐ฆ๐ฌ =โ๐
๐y = ax + b
-3 = โ๐
๐. ๐ + b
b = -2 y = โ๐ฑ
๐- 2
QUESTรO 19.a) A(1, 2) e B(3, 4)
Coeficiente Angular = โ๐
โ๐=
๐ โ๐
๐ โ ๐=
โ๐
โ๐= ๐
y = ax + b2 = 1.1 + bb = 1
y = 1x + 1
QUESTรO 19.b) A(-1, 0) e B(2, 7)
Coeficiente Angular = โ๐
โ๐=
๐ โ๐
โ๐ โ๐=
โ๐
โ๐=
๐
๐
y = ax + b
0 = ๐
๐. -1 + b
b = ๐
๐y =
๐
๐x +
๐
๐
QUESTรO 19.c) A(2, 9) e D(4, -5)
Coeficiente Angular = โ๐
โ๐=
๐ โ(โ๐)
๐ โ ๐=
๐๐
โ๐= -7
y = ax + b9 = -7. 2 + bb = 23
y = -7x + 23
QUESTรO 19.d) A(3, 4) e E(2, -1)
Coeficiente Angular = โ๐
โ๐=
๐ โ(โ๐)
๐ โ๐=
๐
๐= 5
y = ax + b4 = 5.3 + bb = -11 y = 5x - 11
QUESTรO 20.
a) 4x + 3y + 7 = 0
y =โ๐๐
๐-๐
๐
Coef. Angular =โ๐
๐
b) -5x โ 7y + 9 = 0
y =โ๐๐
๐+๐
๐
Coef. Angular =โ๐
๐
c) 3x + 7y โ 9 = 0
y =โ๐๐
๐+๐
๐
Coef. Angular =โ๐
๐
d) 5x โ 4y + 8 = 0
y =๐๐
๐+๐
๐
Coef. Angular =๐
๐
e) 7x + 6y + 9 = 0
y =โ๐๐
๐-๐
๐
Coef. Angular =โ๐
๐
f)A(1, 2) e B(3, 4)๐ โ๐
๐ โ๐=โ๐
โ๐=1
Coef. Angular = 1
g)A(-1, 0) e B(2, 7)๐ โ๐
โ๐ โ ๐=โ๐
โ๐=
๐
๐
Coef. Angular =๐
๐
h)A(2, 9) e D(4, -5)๐ โ(โ๐)
๐ โ๐=๐๐
โ๐= -7
Coef. Angular = -7
i)A(3, 4) e E(2, -1)๐ โ(โ๐)
๐ โ ๐=๐
๐= ๐
Coef. Angular = 5
QUESTรO 21.
a) = 45ยฐCoeficiente Angular = tg 45ยฐ= 1
b) = 120ยฐCoeficiente Angular = tg 120ยฐ= - tg 60ยฐ= โ ๐
c) = 150ยฐ
Coeficiente Angular = tg 150ยฐ = - tg 30ยฐ= -๐
๐
d) = 60ยฐCoeficiente Angular = tg 60ยฐ= ๐
e) = 135ยฐCoeficiente Angular = tg 135ยฐ = - tg 45ยฐ= -1
QUESTรO 22.a) = 45ยฐ e P(1, 2)Coeficiente Angular = tg 45ยฐ= 1
b) = 30ยฐ e P(2, 2)
Coeficiente Angular = tg 30ยฐ=๐
๐
c) = 120ยบ e P(-1, 6)
Coeficiente Angular = tg 120ยฐ= - tg 60ยฐ= โ ๐
y = ax + b
6 = โ ๐.-1 + b
b = 6 โ ๐
y = โ ๐ x + 6 โ ๐
y = ax + b
2 = ๐
๐.2 + b
b = 2 -๐ ๐
๐
y = ๐
๐x + 2 -
๐ ๐
๐
y = ax + b2 = 1.1 + bb = 1
y = 1x + 1
QUESTรO 22.
d) = 60ยบ e P(8, 0)
Coeficiente Angular = tg 60ยฐ= ๐
e) = 150ยบ e P(6, -2)
Coeficiente Angular = tg 150ยฐ = - tg 30ยฐ= -๐
๐
y = ax + b
8 = ๐. 8 + b
b = -8 ๐
y = ๐ x โ๐ ๐
y = ax + b
-2 = -๐
๐.6 + b
b = -2 + 2 ๐y = -
๐
๐x -2 + 2 ๐
QUESTรO 23.a) Como sรฃo paralelas, tem o mesmo coeficiente angular: ms = -2b) -2.ms = -1
ms = 1/2
c)โ๐
๐. ms = -1
ms =๐
๐
d) Como sรฃo paralelas, tem o mesmo coeficiente angular: ms = 2/5
e)๐
๐. ms = -1
ms =โ๐
๐
f)๐
๐. ms = -1
ms =โ๐
๐
QUESTรO 24.
2y โ x โ 5 = 0
y = x/2 + 5/2
y = ax + b
2 = ๐
๐. 1 + b
b = ๐
๐
y = ๐
๐x +
๐
๐
P(1, 2)
QUESTรO 25.
Intersecรงรฃo da reta S com o eixo das abcissas:x โ y โ 4 = 0x โ 0 โ 4 = 0x = 4 e y = 0
x + 2y + 2 = 02y = -x โ 2y = (-1/2)x - 1
y = ax + b
0 = โ๐
๐. 4 + b
b = 2
y = โ๐ฑ
๐+2
QUESTรO 26. C
Nas primeiras 2 horas, a variaรงรฃo foi de 1,5 KmNas 2 horas seguintes, a variaรงรฃo foi de 40 KmNas 2 horas finais, a variaรงรฃo foi de 10 KmO grรกfico que melhor representa estรก na letra C.
QUESTรO 27. C
60 + 40 + 60 + 40 + 20 + 80 = 300
QUESTรO 28.
A) ๐๐ซ๐รง๐จ ๐๐ฆ๐ฆ๐๐ซรง๐จ: ๐ท๐
๐๐ซ๐รง๐จ ๐๐ฆ ๐๐๐ซ๐ข๐ฅ: ๐ท๐
๐ท๐ = ๐ท๐.(1 + 0,3)26 = ๐ท๐.(1 + 0,3)๐ท๐ = R$ 20,00
๐๐ซ๐รง๐จ ๐๐ฆ๐ฆ๐๐ซรง๐จ: ๐ท๐
๐๐ซ๐รง๐จ ๐๐ฆ ๐๐๐ซ๐ข๐ฅ: ๐ท๐
๐ท๐ = ๐ท๐ . (1 + 0,56)๐ท๐= 20 . (1 + 0,56)๐ท๐ = R$ 31,20
B) ๐๐ซ๐รง๐จ ๐๐ฆ๐ฆ๐๐ข๐จ:๐$ ๐๐, ๐๐
๐๐ซ๐รง๐จ ๐๐ฆ ๐๐ฎ๐ง๐ก๐จ: ๐ท๐ = ๐ท๐ . (1 + 0,482) = R$ 29,64
ร๐ง๐๐ข๐๐: ๐ข
i = ๐๐,๐๐ โ๐๐,๐๐
๐๐,๐๐=
โ๐,๐๐
๐๐,๐= โ๐, ๐๐ = โ๐% (๐น๐๐ ๐รงรฃ๐)
QUESTรO 29. D
O nรบmero total de acidentes ocorridos รฉ 12 . 0 + 9 . 1 + 10 . 2 + 5 . 3 + 3 . 4 + 2 . 5 + 1 . 6 = 72. O nรบmero de motoristas que sofreram pelo menos quatro acidentes รฉ 3 + 2 + 1 = 6 > 5. O nรบmero de motoristas que sofreram no mรกximo dois acidentes รฉ 12 + 9 + 10 = 31 > 30.
QUESTรO 30. C
Pelo grรกfico temos que V = รกrea da figura formada no intervalo pedido,
entรฃo V = 1,4.(15 โ 5) = 14 L.
Logo, Q = 4,8.14 = 67,2 kcal.
QUESTรO 31. D
O รบnico grรกfico que se passa retas verticais e nรฃo se toca em dois estรก na letra D. Logo รฉ uma funรงรฃo.
QUESTรO 32. E
f(-3/2) รฉ um valor entre 0 e 1.f(1/2) รฉ um valor entre 2 e 3.Essa soma sรณ poderรก estar entre 2 e 4.
QUESTรO 33.
A) De acordo com o grรกfico, entre 1940 e 1950
B) ๐๐ โ๐
๐๐ โ๐๐= ๐,๐๐ ๐๐๐ ๐๐๐๐๐๐๐๐๐๐ ๐๐๐ ๐๐๐
Sabendo-se que na dรฉcada de 80 a populaรงรฃo รฉ de 10 mil, para se chegar a 20 mil faltam 10 mil pessoas.๐๐
๐, ๐๐โ ๐๐ ๐๐๐๐
Logo, 1980 + 67 = 2047Resposta: Entre 2040 e 2050
QUESTรO 34. B
B) Falsa, pois depois de uma certa quantidadeingerida a absorรงรฃo se mantรฉm constante.
QUESTรO 35. D
QUESTรO 36. E
e)f(2) + f(3) = 2 + 3 = 5f(5) = 4Logo, f(2) + f(3) โ f(5)