Free Printable A2-CHAPTER 6 TEST 2023-2024

1.

a)

$-x^2-4x$

b)

$-2x^2-14x$

c)

$2x+12$

d)

$x^2-x$

2.

a)

$-12x^2-8x$

b)

$x^2+6x$

c)

$x+6$

d)

$2x$

3.

a)

$-2x^2-9x$

b)

$x^{2\ }-6x$

c)

$-x+7$

d)

$2x^2+12x-2$

4.

a)

$-2x^{ }-9x$

b)

$3x^{2\ }-6x\ -5$

c)

$-2x+6$

d)

$2x^2+12x-2$

5.

a)

$-3x^2+4x$

b)

$3x^{2\ }-6x\ -5$

c)

$-2x^2+6$

d)

$2x^2-2$

6.

a)

$-x^2+4x$

b)

$3x^{2\ }-6$

c)

$-2x^2-x$

d)

$2x^2-2$

7.

a)

$-x^2+4x+8$

b)

$x^{2\ }-4x-4$

c)

$-2x^2-x+1$

d)

$2x^2-2x-100$

8.

a)

$-10x+2$

b)

$4x-4$

c)

$x+1$

d)

$-2x-10$

9.

a)

$12x+x$

b)

$4x^2-4$

c)

$-5x^2+4$

d)

$3x^2+x$

10.

a)

$-12x^2-8x$

b)

$-4x^2-6x$

c)

$x+12$

d)

$18x^2-2x$

11.

When f(x) = x²+9 and g(x) = x-9, find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

12.

f(n)=2n+1
g(n)=3n
Find f(n)+g(n)

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

13.

f(n)=x²+1
g(n)=2x-5
Find f(n)-g(n)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

14.

Given the functions f(x) = - 3x²- 2 and g(x) = 3x, find f(x) - g(x).

a)

3x²-3x+2

b)

-2

c)

-3x²-3x-2

d)

-6x-2

15.

f(x) = 4x+8
g(x) = x+3,
Find f(x)*g(x)

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

16.

h(x) = 2x² - x + 1
g(x) = 3x
Find (h*g)(x).

a)

5x³ + 2x² + 3x

b)

2x² + 2x + 1

c)

6x³ - 3x² + 3x

d)

6x³ - 1

17.

$f\left(x\right)\ =\ x^2-5x+8\ \ \ \ \ \ and\ \ \ \ \ g\left(x\right)=\ x^2-4$
Find: $\left(f\cdot g\right)\left(x\right)$

a)

$x^4-5x^3+24x-32$

b)

$x^4-x^2+20x-32$

c)

$x^4-5x^3+4x^2+20x-32$

d)

$x^4-5x^3+12x^2+20x-32$

18.

f(x)=2x + 4

g(x)=3x²- 1

Find f(x) ⋅ g(x)

a)

6x⁴+ 12x³- 4x²- 8x

b)

-6x³+ 12x²+ 2x - 4

c)

6x³+ 12x²- 2x - 4

d)

5x²- 18x + 20

19.

f(x) = 4x + 8

g(x) = x + 3,

Find f(x) ⋅ g(x)

a)

4x²+ 24

b)

4x²+ 20x + 24

c)

4x²+ 12x + 24

d)

4x²+ 4x + 24

20.

f(x)= x³- 3x

g(x)= - 4x + 1

Find f(x) ⋅ g(x)

a)

-4x³-5x²- 3

b)

-4x³+ 2x²- 3x

c)

-4x⁴+ x³+ 12x²- 3x

d)

-4x⁴-x³+ 12x²+3x

21.

If g(x) = 6x + 4 and f(x) = 3, find f(x) * g(x)

a)

18x + 4

b)

9x + 7

c)

6x + 7

d)

18x + 12

22.

Perform the indicated operation.

a)

b)

c)

d)

23.

Perform the indicated operation.

a)

b)

c)

d)

24.

f(x) = 6x² + 3x + 2 and g(x) = x - 7

Find f(x) * g(x)

a)

6x³ - 39x² + 19x + 14

b)

6x³ - 39x² - 21x - 14

c)

6x³ - 39x² - 19x - 14

d)

6x³ - 45x² - 19x + 14

25.

f(x) = 6x² + 3x + 2 and g(x) = x - 7
Find f(x) * g(x)

a)

6x³ - 39x² + 19x - 14

b)

6x³ - 39x² - 21x - 14

c)

6x³ - 39x² - 19x - 14

d)

6x³ - 45x² - 19x + 14

26.

f(x) = 3 and g(x) = -2x + 5
Find f(x) * g(x)

a)

6x + 15

b)

6x - 15

c)

-6x + 15

d)

6x - 8

27.

f(x) = x + 5 and g(x) = x² - 2x + 3
Find f(x) * g(x)

a)

x³ + 3x² - 7x + 15

b)

x³ - 2x² + 15

c)

x³ + 3x² - 10x + 15

d)

x³ - 3x + 15

28.

Simplify.

a)

$\frac{a-4}{a-4}$

b)

$\frac{2\left(a-4\right)}{\left(a+4\right)\left(a-4\right)}$

c)

$\frac{a-4}{a+4}$

d)

1

29.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

30.

What are the restricted values?

a)

x = - 3 and x = 4

b)

x = 3 and x = - 4

c)

x = 3 only

d)

x = - 4 only

31.

Identify the restricted values

a)

x≠-6

b)

x≠-6, 3

c)

x≠3

d)

x≠-18

32.

Factor and cancel out in order to simplify.

a)

$\frac{1}{n-7}$

b)

$n-7$

c)

$\frac{n-6}{n-7}$

d)

$n-6$

33.

Simplify the rational function

a)

$\frac{1}{x+5}$

b)

$\frac{1}{x-5}$

c)

$\frac{x-5}{x+5}$

d)

$\frac{x-5}{(x-5)(x+5)}$

34.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

35.

a)

A

b)

B

c)

C

d)

D

36.

a)

A

b)

B

c)

C

d)

D

37.

a)

A

b)

B

c)

C

d)

D

38.

a)

A

b)

B

c)

C

d)

D

39.

a)

A

b)

B

c)

C

d)

D

40.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

41.

Find g(- 2).

a)

12

b)

-2

c)

-24

d)

18

42.

Evaluate f(x)=-2x+13 for f(10)

a)

-7

b)

1

c)

-8

d)

7

43.

Given
f(x)= 2x² + 5x - 17, find f(-1).

a)

f(-1) = -20

b)

f(-1) = -24

44.

g(a) = 4a + 1

h(a) = -3a + 2

Find g(h(1))

(a)

45.

f(x) = 3x + 10

g(x) = x - 2

Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

-22

46.

f(x) = 5x - 2

g(x) = x + 6

Find g(f(2))

a)

64

b)

38

c)

14

d)

None of these.

47.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

48.

f(x) = 5x - 2

g(x) = x + 6

Find g(f(2))

a)

64

b)

38

c)

14

d)

None of these.

49.

Given f(x) = x + 15

and g(x) = 2x

Find f(g(3))

a)

21

b)

23

c)

36

d)

None of these.

50.

Given f(x) = x - 9

and g(x) = 2x + 1

Find f(g(0))

a)

0

b)

-8

c)

-17

d)

None of these.

51.

f(x) = 3x + 10

g(x) = x - 2

Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

-22

52.

Find g(5)

a)

3375

b)

375

c)

25

d)

45

53.

f(x) = 3x + 10
g(x) = x - 2

Find $\left(fog\right)\left(5\right)$

a)

19

b)

23

c)

-10

d)

None of these.

54.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

55.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

56.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

57.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

58.

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

a)

3x² +5

b)

x² +1

c)

3x² +1

d)

3x² +6

59.

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

a)

10x-1

b)

10x-5

c)

5x²-1

d)

5x²-5

60.

If f(x) = x-1 and g(x) = 2x,

what is and g(f(x)) ?

a)

2x²-1

b)

2x-1

c)

2x-2

d)

x-2

61.

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

a)

10x²

b)

18x² + 4

c)

6x² + 4

62.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

63.

a)

b)

c)

d)

64.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\sqrt{x}$ find $f\left(f\left(x\right)\right)$

a)

$x^4$

b)

$2x^2$

c)

$2x^4$

d)

$x^3$

65.

$If\ f\left(x\right)=2x+1\ \ and\ \ g\left(x\right)=3x+2$

Find\ \left(f\circ g\right)\left(x\right)

a)

f(g(x)) = 6x + 4

b)

f(g(x)) = 6x + 5

c)

f(g(x)) = 5x + 8

d)

f(g(x)) = 5x + 5

66.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

67.

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

a)

10x²

b)

18x² + 4

c)

6x² + 4

68.

If f(x) = x-1 and g(x) = 2x,

what is and g(f(x)) ?

a)

2x²-1

b)

2x-1

c)

2x-2

d)

x-2

69.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

70.

a)

b)

c)

d)

71.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

72.

p(x) = 3x + 4
q(x) = 2x²
Find q(p(x))

a)

6x² + 4

b)

18x²+ 48x + 32

c)

18x² + 32

d)

None of these.

73.

Using f(x) = 5x + 4 and g(x) = x - 3,

Find g(f(x)).

a)

5x + 1

b)

5x - 15

c)

5x - 11

d)

5x + 7

74.

Using f(x) = 4x + 3 and g(x) = x - 2,

Find f(g(x)).

a)

4x - 5

b)

4x - 11

c)

4x + 1

d)

4x + 5

75.

If $f\left(x\right)=2x+3$ and $g\left(x\right)=-3x-4$ , find $f\left(g\left(x\right)\right)$

a)

$-6x^2-17x-12$

b)

$6x^2+x-12$

c)

$-6x-5$

d)

$5x+7$

76.

If $f\left(x\right)=2x+3$ and $g\left(x\right)=-3x-4$ , find $f\left(g\left(x\right)\right)$

a)

$-6x^2-17x-12$

b)

$6x^2+x-12$

c)

$-6x-5$

d)

$5x+7$

77.

If $f\left(x\right)=-2x+3$ and $g\left(x\right)=-3x+2,$ find $f\left[g\left(x\right)\right].$

a)

$-x+1$

b)

$-2x^2$

c)

$6x-1$

d)

$5x+7$

78.

Let $f\left(x\right)=2x^2+12x$ and $g\left(x\right)=x^2-3x-54$ . Find $\left(\frac{f}{g}\right)\left(x\right)$

Simplify (HINT: factor numerator & denominator)

a)

$\frac{2x^2+12x}{x^2-3x-54}$

b)

$\frac{2x}{x-9}$

c)

$\frac{2x}{x+6}$

d)

$\frac{x+6}{x-9}$

79.

Perform the operations. State your final answer in standard form. State any restrictions in the domain.

a)

$\frac{7x+4}{-3x-2};\ x\ne\frac{3}{2}$

b)

$\frac{7x+4}{-3x-2};\ x\ne\frac{2}{-3}$

c)

$\frac{7x+4}{-3x-2};\ x\ne\frac{3}{-2}$

d)

$\frac{7x+4}{-3x-2};\ x\ne\frac{-2}{3}$

80.

When f(x) = x²-9
and g(x) = x+3 ,
find (f/g)(x).

a)

x-3

b)

x+3

c)

x-12

d)

x-6

81.

f(x)=x²-1
g(x)=x-1
Find (f/g)(x)

a)

x+1

b)

x²+1

c)

x

d)

x²-1

82.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

83.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

84.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

85.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

86.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

87.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

88.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(f\circ g\right)\left(2\right)$

a)

$\frac{1}{4}$

b)

$\frac{1}{8}$

c)

$\frac{7}{2}$

d)

8

89.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ g\right)\left(-4\right)$

a)

44

b)

-40

c)

-30

d)

-28

90.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(f\circ g\right)\left(2\right)$

a)

$\frac{1}{4}$

b)

$\frac{1}{8}$

c)

$\frac{7}{2}$

d)

8

91.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\frac{1}{x^2}$ find $\left(f\circ g\right)\left(-1\right)$

a)

$\frac{1}{4}$

b)

$1$

c)

$-1$

d)

$-\frac{1}{4}$

92.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

93.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

94.

p(x) = 3x + 4
q(x) = 2x²
Find p(p(-3))

a)

-9

b)

7

c)

-11

d)

None of these

95.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

96.

a)

9 - 8/3

b)

9 + 8/3

c)

3

d)

1/3

97.

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

a)

3x² +5

b)

x² +1

c)

3x² +1

d)

3x² +6

98.

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

a)

10x-1

b)

10x-5

c)

5x²-1

d)

5x²-5

99.

If f(x) = x-5 and g(x) = 3x²-1,

what is (f ° g)(x) ?

a)

3x²-5

b)

3x²-1

c)

3x²-4

d)

3x²-6

100.

For f(x) = 2x²-1, what is and (f ° f)(-2) ?

a)

7

b)

97

c)

13

d)

6

101.

If f(x) = x-1 and g(x) = 2x,

what is and g(f(x)) ?

a)

2x²-1

b)

2x-1

c)

2x-2

d)

x-2

102.

a)

(3x-1)/3

b)

x-3

c)

x/3

d)

x

103.

a)

Inverse Functions

b)

Not Inverse Functions

104.

a)

Inverse Functions

b)

Not Inverse Functions

105.

a)

Inverse Functions

b)

Not Inverse Functions

106.

a)

Inverse Functions

b)

Not Inverse Functions

107.

a)

Inverse Functions

b)

Not Inverse Functions

108.

a)

Inverse Functions

b)

Not Inverse Functions

109.

a)

Inverse Functions

b)

Not Inverse Functions

110.

a)

Inverse Functions

b)

Not Inverse Functions

111.

a)

Inverse Functions

b)

Not Inverse Functions

112.

a)

Inverse Functions

b)

Not Inverse Functions

113.

Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)

a)

True

b)

False

114.

Was the inverse function found correctly?

a)

no,

b)

yes

115.

Are the following inverses of each other?

a)

True

b)

False

116.

a)

Inverse Functions

b)

Not Inverse Functions

117.

a)

Inverse Functions

b)

Not Inverse Functions

118.

Are f(x) =x+6 and g(x) =x-6 inverses?

a)

Yes

b)

No

119.

$f\left(x\right)\ =\ 5x\ -\ 5$ $g\left(x\right)\ =\ \frac{1}{5}x\ +\ 1$

Use composition of functions to determine if f(x) and g(x) are inverse functions.

a)

yes

b)

no

120.

a)

Inverse Functions

b)

Not Inverse Functions

121.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

122.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = √(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) = ±√(x+5)

d)

f^-1(x) = x² - 5

123.

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

124.

$Find\ the\ inverse\ of\ g\left(x\right)=\left(x-2\right)^2+5$

a)

$g^{-1}\left(x\right)=\sqrt{x+5}-2$

b)

$g^{-1}\left(x\right)=\sqrt{x-5}+2$

c)

$g^{-1}\left(x\right)=\sqrt{x+2}-5$

d)

$g^{-1}\left(x\right)=\sqrt{x-2}+5$

125.

Find the inverse of $f\left(x\right)=\left(\frac{2x+4}{3}\right)^{\frac{1}{3}}$

a)

$f^{-1}\left(x\right)=\frac{x^3-4}{2}$

b)

$f^{-1}\left(x\right)=\frac{2x^3-4}{3}$

c)

$f^{-1}\left(x\right)=\frac{3x^3+4}{2}$

d)

$f^{-1}\left(x\right)=\frac{3x^3-4}{2}$

126.

Verify that f(x) is the inverse of g(x) $f\left(x\right)=\left(\frac{x+9}{5}\right)^{\frac{1}{5}}\ and\ g\left(x\right)=5x^5-9$

a)

Yes

b)

No

127.

Are the relations inverses?

a)

yes

b)

no

128.

Are the relations inverses?

a)

yes

b)

no

129.

Are the relations inverses?

a)

yes

b)

no

130.

Are the graphs inverses?

a)

yes

b)

no

131.

Are the graphs inverses?

a)

yes

b)

no

132.

Are the graphs inverses?

a)

yes

b)

no

133.

Are the graphs inverses?

a)

yes

b)

no

134.

Which of the following points are part of the inverse? Select ALL that apply!

a)

(2,3)

b)

(1,4)

c)

(-8,0)

d)

(-2,5)

e)

(4,-1)

135.

What is the DOMAIN of the INVERSE function?

a)

{-7, -2, -1, 1, 4}

b)

{-6, -3, -2, 0, 3}

c)

{-3, 0, 2, 3, 6}

d)

{-4, -1, 1, 2, 7}

136.

What is the RANGE of the INVERSE function?

a)

{-5, 1, 3, 4}

b)

{-4, -3, -1, 5}

c)

{-4, -2, 0, 7}

d)

{-7, 0, 2, 4}

137.

TRUE OR FALSE:

If the DOMAIN of a function is (-∞, 2], then the DOMAIN of the INVERSE function will also be (-∞, 2].

a)

false

b)

true

138.

TRUE OR FALSE:

If the RANGE of a function is (4, 2], then the DOMAIN of the INVERSE function will also be (4, 2].

a)

false

b)

true

139.

Here is the domain and range for a function:

D: (-∞, ∞)

R: [3, ∞)

What is the domain and range of the inverse?

a)

D: [3, ∞)

R: (-∞, ∞)

b)

D: (-∞, ∞)

R: [3, ∞)

140.

How do you find an inverse?

a)

Switch x and y

b)

Flip the signs on all the x-values

c)

Flip the signs on all the y-values

d)

Do nothing

141.

If f^-1(-25) = 7 then what is f(7) =

a)

25

b)

7

c)

No enough information.

d)

-25

142.

$g\left(x\right)=-7x^5+7$ Find the inverse of the function.

a)

$g^{-1}\left(x\right)=^5\sqrt{\frac{x-7}{7}}$

b)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

c)

$g^{-1}\left(x\right)=^5\sqrt{-\frac{x-7}{7}}$

d)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

143.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

144.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

145.

FInd the inverse of the function.
$f\left(x\right)=\frac{3x-15}{2}$

a)

$f^{-1}\left(x\right)=-x-5$

b)

$f^{-1}\left(x\right)=3x+5$

c)

$f^{-1}\left(x\right)=\frac{15+2x}{3}$

d)

$f^{-1}\left(x\right)=\frac{2}{3}x-\frac{19}{3}$

146.

Which of the following is the inverse of f(x)= 2x² +6

a)

b)

c)

d)

147.

FIND THE INVERSE

(a)

148.

FIND THE INVERSE

(a)

149.

FIND THE INVERSE

(a)

150.

FIND THE INVERSE

(a)

151.

FIND THE INVERSE

(a)

152.

FIND THE INVERSE

(a)

153.

FIND THE INVERSE

(a)

154.

FIND THE INVERSE

(a)

155.

FIND THE INVERSE

(a)

156.

FIND THE INVERSE

(a)

A2-CHAPTER 6 TEST 2023-2024

Total questions: 156

Worksheet time: 12hrs 32mins

Similar Resources on Wayground