Deck 2: Functions and Linear Functions

Question 1

Find the domain and range.
{(41, -4), (5, -3), (5, 0), (14, 3), (30, 5)}

A) domain: {41, 14, 5, 30}; range: {-4, -3, 3, 5}
B) domain: {-4, -3, 3, 5}; range: {41, 14, 5, 30}
C) domain: {-4, -3, 0, 3, 5}; range: {41, 14, 5, 30}
D) domain: {41, 14, 5, 30}; range: {-4, -3, 0, 3, 5}

Answer 1

D

Question 2

Decide whether the relation is a function.
{(-4, 6), (-1, 6), (2, 9), (6, 5)}

A) not a function
B) function

Answer 2

B

Question 3

Decide whether the relation is a function.
{(-3, 5), (1, 2), (6, -4), (8, 3), (10, 7)}

A) function
B) not a function

Answer 3

A

Question 4

Find the domain and range.
{(-4,4), (3,-5), (-6,-3), (-6,-4)}

A) domain = {-3, 4, -5, -4}; range = {-6, -4, 3}
B) domain = {-6, -4, 3}; range = {-3, 4, -5, -4}
C) domain = {-6, -4, 3, -16}; range = {-3, 4, -5, -4}
D) domain = {-6, -4, 3, 6}; range = {-3, 4, -5, -4}

Question 5

Decide whether the relation is a function.
{(3, 6), (3, 4), (5, -2), (7, -5), (11, 6)}

A) function
B) not a function

Question 6

Find the domain and range.
{(6,-6), (-4,7), (9,8), (9,-1)}

A) domain = {8, 7, -6, -1}; range = {9, -4, 6}
B) domain = {9, -4, 6, 19}; range = {8, 7, -6, -1}
C) domain = {9, -4, 6}; range = {8, 7, -6, -1}
D) domain = {9, -4, 6, -9}; range = {8, 7, -6, -1}

Question 7

Decide whether the relation is a function.
{(-3, 5), (1, 5), (5, 5), (8, -6), (10, -2)}

A) function
B) not a function

Question 8

Find the domain and range.
{(-2,-1), (-8,-7), (12,-2), (8,6)}

A) domain = {8, -8, -2, 12}; range = {6, 6, -7, -1, -2}
B) domain = {8, -8, -2, 12}; range = {6, 1, -7, -1, -2}
C) domain = {6, -7, -1, -2}; range = {8, -8, -2, 12}
D) domain = {8, -8, -2, 12}; range = {6, -7, -1, -2}

Question 9

Find the domain and range.
{(9,-6), (9,-2), (6,-9), (-11,6), (-10,-8)}

A) domain = {9, 12, -11, -10, 6}; range = {-2, 6, -8, -9, -6}
B) domain = {9, -2, -11, -10, 6}; range = {-2, 6, -8, -9, -6}
C) domain = {9, -11, -10, 6}; range = {-2, 6, -8, -9, -6}
D) domain = {-2, 6, -8, -9, -6}; range = {9, 9, -11, -10, 6}

Question 10

Decide whether the relation is a function.
{(-3, 6), (-1, -6), (2, 9), (2, 4)}

A) function
B) not a function

Question 11

Decide whether the relation is a function.
{(-9, 3), (-9, 7), (-1, 5), (5, 1), (9, -6)}

A) function
B) not a function

Question 12

Decide whether the relation is a function.
Find f(4) when f(x) = 5x² + 2x + 2.

A) 90
B) 86
C) 26
D) 74

Question 13

Decide whether the relation is a function.
Find f(1) when f(x) = 8x - 6.

A) 7.4
B) -14
C) 2
D) 14

Question 14

Decide whether the relation is a function.
{(-3, -9), (-1, -8), (4, 9), (5, 1)}

A) function
B) not a function

Question 15

Decide whether the relation is a function.
{(-7, 1), (-7, 4), (1, -8), (3, 9), (9, -3)}

A) function
B) not a function

Question 16

Decide whether the relation is a function.
{(-8, 9), (-4, 3), (-2, -9), (4, 7)}

A) not a function
B) function

Question 17

Find the domain and range.
{(6,-8), (1,3), (-9,-9), (-2,2), (5,-6)}

A) domain = {6, -8, 5, -6, -9}; range = {-9, 1, 3, -2, 2}
B) domain = {-8, -6, -9, 3, 2}; range = {6, 5, -9, 1, -2}
C) domain = {-9, 1, 3, -2, 2}; range = {6, -8, 5, -6, -9}
D) domain = {6, 5, -9, 1, -2}; range = {-8, -6, -9, 3, 2}

Question 18

Decide whether the relation is a function.
{(-5, -2), (-2, -4), (3, -1), (3, 7)}

A) function
B) not a function

Question 19

Find the domain and range.
{(-3, 10), (-2, 5), (0, 1), (2, 5), (4, 17)}

A) domain: {10, 5, 1, 17}; range: {-3, -2, 2, 4}
B) domain: {10, 5, 1, 17}; range: {-3, -2, 0, 2, 4}
C) domain: {-3, -2, 0, 2, 4}; range: {10, 5, 1, 17}
D) domain: {-3, -2, 2, 4}; range: {10, 5, 1, 17}

Question 20

Decide whether the relation is a function.
Find f(2) when f(x) = x² + 3x - 3.

A) 13
B) 7
C) -5
D) 1

Question 21

Decide whether the relation is a function.
A) $g$ shifts the graph of $f$ vertically
down 2 units

B) $g$ shifts the graph of $\mathrm { f }$ vertically
up 2 units


C) g shifts the graph of $f$ vertically
down 2 units

D) $g$ shifts the graph of $f$ vertically
up 2 units

Question 22

Decide whether the relation is a function.
$$f ( x ) = 3 x ^ { 2 } , g ( x ) = 3 x ^ { 2 } - 4$$

A) $g$ shifts the graph of $f$ vertically
down 4 units

B) $g$ shifts the graph of $f$ vertically
down 4 units

C) $g$ shifts the graph of $f$ vertically
up 4 units

D) g shifts the graph of $f$ vertically
up 4 units

Question 23

Decide whether the relation is a function.
A) $g$ shifts the graph of $f$ vertically
up 4 units

B) g shifts the graph of $f$ vertically
down 4 units

C) g shifts the graph of $f$ vertically
up 4 units

D) $g$ shifts the graph of $f$ vertically
down 4 units

Question 24

Decide whether the relation is a function.
A) $g$ shifts the graph of $f$ vertically
down 3 units

B) $g$ shifts the graph of $f$ vertically
up 3 units

C) g shifts the graph of $f$ vertically
up 3 units

D) $g$ shifts the graph of $f$ vertically
down 3 units

Question 25

Decide whether the relation is a function.
$$f ( x ) = x ^ { 2 } , g ( x ) = x ^ { 2 } - 3$$

A) g shifts the graph of f vertically
up 3 units

B) g shifts the graph of $f$ vertically
up 3 units

C) g shifts the graph of f vertically
down 3 units

D) g shifts the graph of $f$ vertically
down 3 units

Question 26

Decide whether the relation is a function.
Find f(6) when f(x) = 6.

A) 6
B) -3
C) -18
D) 0

Question 27

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) not a function
B) function

Question 28

Decide whether the relation is a function.
$$f ( x ) = x ^ { 3 } , g ( x ) = x ^ { 3 } + 2$$

A) $g$ shifts the graph of $f$ vertically
up 2 units

B) $g$ shifts the graph of $f$ vertically
down 2 units

C) $g$ shifts the graph of $f$ vertically
up 2 units

D) g shifts the graph of $f$ vertically
down 2 units

Question 29

Decide whether the relation is a function.
A) g shifts the graph of f vertically
down 2 units

B) g shifts the graph of f vertically
up 2 units

C) g shifts the graph of f vertically
up 2 units

D) g shifts the graph of f vertically
down 2 units

Question 30

Decide whether the relation is a function.
$$f ( x ) = | x | , g ( x ) = | x | + 2$$

A) g shifts the graph of f vertically
down 2 units

B) $g$ shifts the graph of $f$ vertically
up 2 units

C) $g$ shifts the graph of f vertically
up 2 units

D) $g$ shifts the graph of $f$ vertically
down 2 units

Question 31

Decide whether the relation is a function.
A) $g$ shifts the graph of $f$ vertically
up 2 units

B) $g$ shifts the graph of $f$ vertically
down 2 units

C) g shifts the graph of $f$ vertically
down 2 units

D) $g$ shifts the graph of $f$ vertically
up 2 units

Question 32

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) not a function
B) function

Question 33

Decide whether the relation is a function.
Find $f ( 2 )$ when $f ( x ) = \frac { x ^ { 3 } - 5 } { x ^ { 2 } - 3 }$

A) $\frac { 3 } { 4 }$
B) 3
C) 8
D) $- 1$

Question 34

Decide whether the relation is a function.
Find f(0) when f(x) = x² - 5x - 4.

A) 4
B) 0
C) 16
D) -4

Question 35

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) not a function
B) function

Question 36

Decide whether the relation is a function.
A) $g$ shifts the graph of $f$ vertically
down 3 units

B) g shifts the graph of $f$ vertically
down 3 units

C) $g$ shifts the graph of $f$ vertically
up 3 units

D) $g$ shifts the graph of $f$ vertically
up 3 units

Question 37

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) function
B) not a function

Question 38

Decide whether the relation is a function.
Find $f ( - 2 )$ when $f ( x ) = \frac { x ^ { 2 } - 2 } { x ^ { 3 } - 2 x }$ .

A) $- \frac { 1 } { 4 }$
B) $- \frac { 1 } { 2 }$
C) $- \frac { 1 } { 5 }$
D) - 1

Question 39

Decide whether the relation is a function.
A) $g$ shifts the graph of $f$ vertically
down 4 units

B) $g$ shifts the graph of f vertically
up 4 units

C) g shifts the graph of $f$ vertically
up 4 units

D) g shifts the graph of $f$ vertically
down 4 units

Question 40

Decide whether the relation is a function.
Find g(a - 1) when g(x) = 4x - 4.

A) 4a - 4
B) 4a
C) 4a - 8
D) 4a - 12

Question 41

Use the graph to identify domain and range.
A) domain: $[ - 1 , \infty )$
range: $( \infty , \infty )$
B) domain: $( - 1 , \infty )$
range: $( \infty , \infty )$
C) domain: $( \infty , \infty )$
range: $( - 1 , \infty )$
D) domain: $( \infty , \infty )$
range: $[ - 1 , \infty )$

Question 42

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) function
B) not a function

Question 43

Use the graph to find the indicated function value.
y = f(x). Find f(-4)

A) 1.75
B) 4
C) 13
D) -4

Question 44

Find the domain of the function.
$$f ( x ) = \frac { 1 } { x - 9 }$$

A) $( 9 , \infty )$
B) $( \infty , \infty )$
C) $( \infty , 0 )$ or $( 0 , \infty )$
D) $( \infty , 9 )$ or $( 9 , \infty )$

Question 45

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question.

Between what two years is the difference in function values equal to 5%?

A) between 1995 and 2000
B) between 1980 and 1985
C) between 1970 and 1975
D) between 1990 and 1995

Question 46

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question.

If f(x) = 20%, what year is represented by x?

A) 2000
B) 1985
C) 1995
D) 1990

Question 47

Use the graph to find the indicated function value.
y = f(x). Find f(4).

A) 4
B) 1.75
C) 13
D) -4

Question 48

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) function
B) not a function

Question 49

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) function
B) not a function

Question 50

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question.

If f represents the function, find f(2010).

A) approximately 31%
B) approximately 25.5%
C) approximately 24%
D) approximately 29%

Question 51

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) not a function
B) function

Question 52

Find the domain of the function.
$$f ( x ) = 7 x + 5$$

A) $( - 5 , \infty )$
В) $( \infty , 0 )$ or $( 0 , \infty )$
C) $( \infty , \infty )$
D) $( x , - 5 )$ or $( - 5 , \infty )$

Question 53

Use the graph to identify domain and range.
A) domain: $[ 0,8 ]$
range: $( \infty , \infty )$
B) domain: $( \infty , \infty )$
range: $[ 0,8 ]$
C) domain: $[ 3,8 ]$
range: $( \infty , \infty )$
D) domain: $( \infty , \infty )$
range: $[ 3,8 ]$

Question 54

Use the graph to find the indicated function value.
y = f(x). Find f(3)

A) 1
B) -7
C) 5
D) 7

Question 55

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) not a function
B) function

Question 56

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) function
B) not a function

Question 57

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) not a function
B) function

Question 58

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question.

Does the graph represent a function?

A) no
B) yes

Question 59

Use the graph to find the indicated function value.
y = f(x). Find f(-4)

A) 4
B) 0
C) 9
D) 3

Question 60

Use the vertical line test to determine whether or not the graph is a graph of a function.

A) function
B) not a function

Question 61

Find the indicated function value.
$$f ( x ) = 4 x + 5 , g ( x ) = - 4 x + 3$$
Find $( f + g ) ( - 1 )$ .

A) 8
B) $- 6$
C) 5
D) 4

Question 62

For the pair of functions, determine the domain of f + g.
$$f ( x ) = 5 x - 1 , g ( x ) = \frac { 4 } { x - 2 }$$

A) $( \infty , \infty )$
B) $( 0 , \infty )$
C) $( x , - 4 )$ or $( - 4 , \infty )$
D) $( \infty , 2 )$ or $( 2 , \infty )$

Question 63

Find the indicated function value.
$$f ( x ) = 3 x - 1 , g ( x ) = 2 x ^ { 2 } - 1$$
Find $( f + g ) ( 3 )$ .

A) 26
B) 27
C) 25
D) 19

Question 64

Find the domain of the function.
$$f ( x ) = \frac { 1 } { x - 5 } + \frac { 4 } { x + 10 }$$

A) $( \infty , - 5 )$ or $( - 5,10 )$ or $( 10 , \infty )$
B) $( \infty , - 10 )$ or $( - 10,5 )$ or $( 5 , \infty )$
C) $( \infty , \infty )$
D) $( \infty , - 10 )$ or $( 5 , \infty )$

Question 65

Find the domain of the function.
$$f ( x ) = x - \frac { 7 } { x - 3 }$$

A) $( \infty , 7 )$ or $( 7 , \infty )$
B) $( \infty , \infty )$
C) $( \infty , 0 )$ or $( 0 , \infty )$
D) $( \infty , 3 )$ or $( 3 , \infty )$

Question 66

Find the domain of the function.
$$f ( x ) = \frac { x } { x ^ { 2 } + 8 }$$

A) $( \infty , - 8 )$ or $( - 8 , \infty )$
B) $( \infty , 0 )$ or $( 0 , \infty )$
C) $( - 8 , \infty )$
D) $( \infty , \infty )$

Question 67

For the pair of functions, determine the domain of f + g.
$$f ( x ) = 3 x ^ { 2 } + 1 , g ( x ) = 5 x ^ { 3 } - 7$$

A) $( \infty , \infty )$
B) $( \infty , 0 )$
C) $( 0 , \infty )$
D) $( \infty , 0 )$ or $( 0 , \infty )$

Question 68

For the pair of functions, determine the domain of f + g.
$$f ( x ) = \frac { 2 x } { x - 1 } , g ( x ) = \frac { 4 } { x + 9 }$$

A) $( \infty , \infty )$
B) $( \infty , - 9 )$ or $( 1 , \infty )$
C) $( \infty , - 1 )$ or $( - 1,9 )$ or $( 9 , \infty )$
D) $( - \infty , - 9 )$ or $( - 9,1 )$ or $( 1 , \infty )$

Question 69

Find the requested value.
$$f ( x ) = - 5 x ^ { 2 } - 5 x + 8 , g ( x ) = 3 x - 8$$
Find $f ( - 2 ) + g ( - 2 )$ .

A) 24
B) 2
C) 26
D) $- 16$

Question 70

For the pair of functions, determine the domain of f + g.
$$f ( x ) = 5 x + 5 , g ( x ) = \frac { 3 } { x + 1 }$$

A) $( \infty , \infty )$
B) $( 0 , \infty )$
C) $( \infty , - 3 )$ or $( - 3 , \infty )$
D) $( - , - 1 )$ or $( - 1 , \infty )$

Question 71

Find the domain of the function.
$$f ( x ) = \frac { - 5 x } { x + 3 }$$

A) $( \infty , - 3 )$ or $( - 3 , \infty )$
B) $( \infty , \infty )$
C) $( - , - 3 )$
D) $( x , 0 )$ or $( 0 , \infty )$

Question 72

Find the indicated function value.
$$f ( x ) = 2 x ^ { 2 } - 2 , g ( x ) = 3 x ^ { 2 } + 3 x - 3$$
Find $( f + g ) ( 4 )$ .

A) 63
B) 93
C) 51
D) 87

Question 73

Find the indicated function value.
$$f ( x ) = 9 - 7 x , g ( x ) = - 3 x + 7$$
Find $( f + g ) ( x )$ .

A) $- 10 x + 16$
B) $6 x$
C) $- 3 x + 9$
D) $- 4 x + 16$

Question 74

Find the requested value.
$$f ( x ) = - 3 x ^ { 2 } - 4 , g ( x ) = x - 1$$
Find $f ( - 4 ) - g ( - 4 )$ .

A) $- 47$
B) 56
C) $- 55$
D) $- 49$

Question 75

Find the indicated function value.
$$f ( x ) = 2 x - 5 , g ( x ) = 2 x ^ { 2 } + 2 x - 1$$
Find $( f + g ) ( 4 )$ .

A) 42
B) 26
C) 34
D) 36

Question 76

Find the indicated function value.
$$f ( x ) = x ^ { 2 } + \frac { 1 } { 3 } x - 3 , g ( x ) = x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } + x$$
Find $( f + g ) ( x )$ .

A) $x ^ { 3 } + \frac { 1 } { 3 } x ^ { 2 } + \frac { 4 } { 3 } x - 3$
B) $2 x ^ { 3 } - \frac { 1 } { 6 } x ^ { 2 } - 2 x$
C) $x ^ { 3 } + \frac { 1 } { 6 } x ^ { 2 } + \frac { 2 } { 3 } x - 3$
D) $2 x ^ { 3 } - \frac { 1 } { 3 } x ^ { 2 } - 2 x$

Question 77

Find the indicated function value.
$$f ( x ) = 4 x ^ { 2 } - 4 , g ( x ) = 2 x ^ { 2 } - 2$$
Find $( f + g ) ( 5 )$ .

A) 148
B) 48
C) 144
D) 104

Question 78

Find the domain of the function.
$$f ( x ) = x ^ { 2 } + 8$$

A) $[ - 8 , \infty )$
B) $( \infty , - 8 )$ or $( - 8 , \infty )$
C) $( - 8 , \infty )$
D) $( \infty , \infty )$

Question 79

Find the indicated function value.
$$f ( x ) = x + 2 , g ( x ) = x + 7$$
Find $( f + g ) ( 1 )$ .

A) 11
B) $- 7$
C) 7
D) $- 3$

Question 80

Find the indicated function value.
$$f ( x ) = 5 x ^ { 2 } + 7 x + 6 , g ( x ) = 3 x + 4$$
Find $( f + g ) ( 5 )$ .

A) 245
B) 261
C) 185
D) $- 65$