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HA2 Function Review

Total questions: 65

Worksheet time: 4hrs 42mins

Name
Class
Date
1.

Perform the indicated operation.

a)
b)
c)
d)
2.

Perform the indicated operation.

a)
b)
c)
d)
3.

Complete the operation and evaluate.

a)
b)
c)
d)
4.

Perform the indicated operation.

a)
b)
c)
d)
5.

Perform the indicated operation.

a)
b)
c)
d)
6.

Perform the indicated operation and evaluate for the given value.

a)
b)
c)
d)
7.

Perform the indicated operation.

a)
b)
c)
d)
8.

Perform the indicated operation.

a)
b)
c)
d)
9.

Perform the indicated operation and evaluate at the given value.

a)
b)
c)
d)
10.

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

11.
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
12.
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
13.
f(x) = x2+9
g(x) = x-9
Find f(x)-g(x). 
a)
x2+x+9
b)
x2-x+9
c)
x2-x
d)
x2-x+18
14.

When f(x) = 9 - 3x and g(x) = 5x - 7

find f(x) + g(x).

a)

14x - 10

b)

-8x + 2

c)

2x + 2

d)

2x - 2

15.

Given f(x) = -x + 4 and g(x) = 6x + 3, find (f(x) - g(x))

a)

-7x + 1

b)

5x +1

c)

-5x -1

d)

5x + 1

16.

f(x)= x2 - 1

g(x)= x - 1

Find (f(x)/g(x))

Then simplify using x = 10

a)

9

b)

11

c)

90

d)

110

17.
f(x)=3x2+1
g(x)=4x+5
What is (f+g)(2)
a)
13
b)
0
c)
26
d)
6x2+8x+12
18.
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1,
 find (f - g)(x).
a)
x2 + 8x + 1
b)
x2 + 6x - 1
c)
5x2 + 8x - 1
d)
x2 + 8x -1
19.
When f(x) = 2x and g(x) = x2+3 , find f(g(x)).
a)
x2+2x+3
b)
4x2+3
c)
2x2+3
d)
2x2+6
20.
When f(x) = x2 -9 
and g(x) = x+3 ,
find f(x) / g(x). 
a)
x-3
b)
x+3
c)
x-12
d)
x-6
21.

f(x) = 3x - 1

g(x) = 2x + 4

Find f(g(x))

a)

6x+11

b)

6x + 13

c)

6x2 - 12

d)

5x + 6

22.

f(x) = 3x - 1

g(x) = 2x + 4

Find g(f(x))

a)

6x+11

b)

6x + 2

c)

6x2 - 12

d)

5x + 6

23.
When f(x) = 2x and g(x) = x2+3 , find f(g(x)).
a)
x2+2x+3
b)
4x2+3
c)
2x2+3
d)
2x2+6
24.

When f(x) = 2x and g(x) = x2+3 , find g(f(x)).

a)

x2+2x+3

b)

4x2+3

c)

2x2+3

d)

2x2+6

25.
p(x) = 3x + 4
q(x) = 2x2
Find p(q(x))
a)
10x2
b)
18x2 + 4
c)
6x2 + 4
26.
g(x)=3x+4
h(x)=3x-1
Find g(h(x))
a)
-9x+11
b)
4x2+4x
c)
9x+1
d)
9x+11
27.

Given f(x)= (2 + x )2, what is the value of f(-3)?

a)

1

b)

25

c)

-1

d)

5

28.

Given f(x) = 3(6 -x), what is the value of f(-8)

a)

-42

b)

6

c)

-6

d)

42

29.

Given f(x) = x2 - 1, what is the value of f(10)?

a)

100

b)

101

c)

99

d)

9

30.
p(x) = 3x + 4
q(x) = 2x2
Find p(p(-3))
a)
-9
b)
7
c)
-11
d)
None of these
31.
p(x) = 3x + 4
q(x) = 2x2
Find p(q(x))
a)
10x2
b)
18x2 + 4
c)
6x2 + 4
32.
Given f(x) = x2 - 3 and g(x) = x - 3, find f(g(f(3))).
a)
0
b)
3
c)
6
d)
9
33.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

34.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

35.

g(a) = 4a + 1

h(a) = -3a + 2

Find g(h(1))

a)

3

b)

-3

c)

21

d)

-21

36.
p(x) = 3x + 4
q(x) = 2x2
Find q(p(-2))
a)
8
b)
-8
c)
28
d)
None of these.
37.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

38.
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
39.

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

a)

True

b)

False

40.
Was the inverse function found correctly?
a)
no,
b)
yes
41.
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
42.
Find the inverse of the function
f(x) = 3x − 5
a)
f-1(x)=3x +5
b)
f-1(x)=(x+5)/3
c)
f-1(x)=3y-5
d)
f-1(x)=3y+5
43.
What does it mean to find the inverse of a function?
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
44.

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

a)

(x + 5)2

b)

x - 5

c)

(x + 5)-1

d)

undefined

45.

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

a)

x/3

b)

3x2

c)

3x + 3x

d)

3x-1

46.
a)

Inverse Functions

b)

Not Inverse Functions

47.
a)

Inverse Functions

b)

Not Inverse Functions

48.
a)

Inverse Functions

b)

Not Inverse Functions

49.
a)
Inverse Functions
b)
Not Inverse Functions
50.

What operation allows us to verify if functions are inverses?

a)

Multiplying

b)

Dividing

c)

Adding

d)

Composing

51.
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)
52.
a)
9 - √17
b)
4
c)
2
d)
√8
53.
The composition of any function, f(x), and
its inverse, f-1(x) = 
a)
x
b)
f(x)
c)
1
d)
0
54.
The inverse of the function f(x) is written as ...
a)
f -1(x)
b)
f 2(x)
c)
f '(x)
d)
f +(x)
55.
The inverse has been reflected over which line?
a)
y = x
b)
x = 0
c)
y = 0
d)
x = -y
56.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function always becomes the domain of its inverse.

d)

The domain of a function always becomes the range of its inverse.

57.
What are the missing values if g(x)=f-1(x)?
a)
(9,-5)
b)
(-9,-5)
c)
(5,9)
d)
(-9,5)
58.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

59.

Which graph represents f-1(x) over the same domain?

a)
b)
c)
d)
60.

Which graph represents the functions f(x) and f-1(x)?

a)
b)
c)
d)
61.
What color are the Smurfs?
a)
Green
b)
Purple
c)
Blue
d)
Red
62.
How many colors are in a rainbow?
a)
100
b)
10
c)
7
d)
70
63.
 Who does the animated character Princess Fiona marry?
a)
Shrek
b)
Donkey
c)
Prince Charming
d)
Prince Phillip
64.
How many years are in a century?
a)
1000
b)
1
c)
10
d)
100
65.
Cruella De Vil is from what movie?
a)
Beauty and the Beast 
b)
Alice in Wonderland 
c)
101 Dalmatians 
d)
Lion King

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