Free Printable Unit 1 Functions & Inverses

1.

Given g(x) = 4x - 7, find g(-9).

a)

g(-9) = 29

b)

g(-9) = -43

c)

g(-9) = 43

d)

g(-9) = -29

2.

a)

F

b)

G

c)

H

d)

J

3.

What is the Domain?

a)

-10 ≤ y ≤ 6

b)

y ≤ 6

c)

-10 ≤ x ≤ 6

d)

All Real Numbers

4.

What is the domain of the graph?

a)

-3 ≤ x ≤ 3

b)

3 ≤ x ≤ -3

c)

-2 ≤ x ≤ 10

d)

-3 ≤ x ≤ 10

5.

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

a)

19

b)

23

c)

-10

d)

None of these.

6.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

7.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

8.

Is this a function?

a)

Function

b)

Not a Function

9.

Find (f + g)(x)

a)

2x - 4

b)

8x - 4

c)

8x + 20

d)

2x + 4

10.

Find (f − g)(x)

a)

2x - 4

b)

8x + 4

c)

8x - 20

d)

2x + 4

11.

a)

24

b)

$80$

c)

$72$

d)

$16$

12.

a)

25

b)

$-48$

c)

$61$

d)

$-12$

13.

a)

144

b)

$25$

c)

$156$

d)

$78$

14.

h(x) = -4x + 3

g(x) = 4x - 2

Find h(g(6))

a)

-107

b)

107

c)

-85

d)

85

15.

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

a)

$f^{-1}(x)=4x-3$

b)

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

c)

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

d)

$f^{-1}(x)=-4x-3$

16.

Find the inverse of f(x) = 3x +8

a)

$f^{-1}(x)=3(x-8)$

b)

$f^{-1}(x)=\frac{8x-1}{3}$

c)

$f^{-1}(x)=\frac{x-8}{3}$

d)

$f^{-1}(x)=\frac{x+8}{3}$

17.

If a function has the point (4,-2) then its inverse must have which point?

a)

(-4,-2)

b)

(-4,2)

c)

(-2,4)

d)

(2,-4)

18.

f(x) = 3x + 10

g(x) = x - 2

Find g(f(6))

a)

26

b)

28

c)

-10

d)

None of these.

19.

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)

20.

Which step comes first when solving for the inverse of a function?

a)

get x by itself

b)

switch x and y

c)

solve for y

d)

write the function in inverse function notation

21.

What is the inverse of the function

f(x) = 2x + 4 ?

a)

$f^{-1}(x)=4(x-2)$

b)

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

c)

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

d)

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

22.

What does it mean to find the inverse of a function when we are looking at tables?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

23.

When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

a)

solve for y

b)

replace y with f^-1(x)

c)

solve for x

d)

find the greatest common factor

24.

Find the inverse of
$f(x)=\frac{1}{4}x-7$

a)

$f^{-1}(x)=4x+7$

b)

$f^{-1}(x)=-4x+28$

c)

$f^{-1}(x)=-4x-7$

d)

$f^{-1}(x)=4x+28$

25.

Given f(x) = 3x + 2 and g(x) = 6x - 8, which is the correct set up for f(g(x))?

a)

6(3x+2) - 8

b)

3(6x-8) + 2

c)

3x(6x-8) + 2

d)

6x(3x+2) - 8

26.

Given $f(x)=2x+9$ and g(x) = $x^2\ -\ 3$ , which is the correct set up for g(f(x))?

a)

$2\left(x^2\ -\ 3\right)+9$

b)

$2x\left(x^2-3\right)+9$

c)

$\left(2x+9\right)^2-3$

d)

$x\left(2x+9\right)^2-3$

27.

What is the domain of this function?

a)

[-4, 5)

b)

(-4, 5]

c)

[-4, 5]

d)

(-4, 5)

28.

What is the range of this function?

a)

$-3<x<3$

b)

$-3\le x\le3$

c)

$-3<y<3$

d)

$-3\le y\le3$

29.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

30.

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)

31.

Which expression represents g(f(x)) if f(x) = 2x - 8
and
g(x) = 4x

a)

8x - 32

b)

8x² - 32x

c)

8x - 8

d)

6x - 8

32.

If f(x)=x+5, what is f^-1(x)?

a)

(x + 5)²

b)

x - 5

c)

(x + 5)^-1

d)

undefined

33.

If f(x)=3x, what is f^-1(x)?

a)

$\frac{x}{3}$

b)

$3x^2$

c)

$3x$

d)

$x-3$

34.

Which is not a function?

a)

b)

c)

d)

35.

What is the domain in interval notation?

a)

[ -5 , 5 )

b)

{ -5 ≤ x < 5 }

c)

{ -8 < x ≤ 5 }

d)

( -8 , 5 ]

36.

Which image represents a relation and its inverse?

a)

b)

c)

d)

37.

Which shows the correct composition for finding (ƒ ° g) (x) ?

ƒ (x) = 4x

g(x) = 3x + 1

a)

(ƒ°g)(x) =4x(3x+1)

b)

(ƒ°g)(x) = 3(4x)+1

c)

(ƒ°g)(x) = 4(3x+1)

d)

(ƒ°g)(x) = 3x(4x)+1

38.

$f(x)=-5x+8$

If $f(4)=-12$ , then what is $f^{-1}(-12)$ ?

a)

-12

b)

68

c)

No enough information.

d)

4

39.

Are these functions inverses?

a)

Yes

b)

No

40.

Are these inverse functions?

a)

no

b)

yes

c)

no way to tell

41.

Are the blue and red graphs inverse functions?

a)

yes

b)

no

c)

no way to tell

42.

Find the inverse of $f\left(x\right)=3x+2$

a)

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

b)

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

c)

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

d)

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

43.

Identify the range of the following function when given the domain { 2, 3, 10}:

y = 4x - 12

a)

{4, 12, 20}

b)

{-20, 0, 28}

c)

{-4, 0, 28}

d)

{8, 12, 40}

44.

What is the range of the following graph?

a)

{-5, -1, 0 , 1, 5}

b)

{-4, -2, 0, 3, 6}

c)

(-4, 1) ( 6, 0)

d)

(6, 0)

45.

What is the Domain of this linear function?

a)

-3 < x ≤ 5

b)

x = -1

c)

5 < x ≤ -3

d)

-2 < x ≤ 6

46.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

47.

Which mapping diagram is not a function?

a)

b)

c)

d)

48.

Which graph is not a function?

a)

b)

c)

d)

49.

What is the range of the graph?

a)

-7 ≤ x < 5

b)

-3 ≤ x < 1

c)

-3 ≤ y < 1

d)

-7 ≤ y < 5

50.

What is the DOMAIN of this graph?

a)

x < -3

b)

x ≤ -3

c)

x > -3

d)

x ≥ -3

Unit 1 Functions & Inverses

Total questions: 50

Worksheet time: 2hrs 43mins

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