Deck 8: Basics of Functions

Question 1

Decide whether the relation is a function.
Women's Shoe Sizes $$\begin{array} { l | c c c c c c c } \text { USA } & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \text { Japan } & 20 & 21 & 22 & 23 & 24 & 25 & 26\end{array}$$

A) function
B) not a function

Answer 1

function

Question 2

Decide whether the relation is a function.
$$\{ ( 3 , - 3 ) , ( 3,3 ) , ( 6,9 ) , ( 8,8 ) , ( 10 , - 7 ) \}$$

A) function
B) not a function

Answer 2

not a function

Question 3

Decide whether the relation is a function.

-Tallest Roller Coaters in U.S. Amusement Parks $$\begin{array} { l | l l l l l l } \text { Amusement Park Name } & \text { Park A } & \text { Park A } & \text { Park B } & \text { Park C } & \text { Park B } & \text { Park A } \\\hline \text { Coaster Height (feet) } & 72 & 69 & 65 & 64 & 60 & 57\end{array}$$

A) function
B) not a function

Answer 3

not a function

Question 4

Find the domain and range.
$$\{ ( 1 , - 2 ) , ( - 3 , - 1 ) , ( - 3,0 ) , ( - 2,1 ) , ( 6,3 ) \}$$

A) domain: $\{ 1 , - 2 , - 3,6 \}$ ; range: $\{ - 2 , - 1,1,3 \}$
B) domain: $\{ - 2 , - 1,1,3 \}$ ; range: $\{ 1 , - 2 , - 3,6 \}$
C) domain: $\{ - 2 , - 1,0,1,3 \}$ ; range: $\{ 1 , - 2 , - 3,6 \}$
D) domain: $\{ 1 , - 2 , - 3,6 \}$ ; range: $\{ - 2 , - 1,0,1,3 \}$

Question 5

Find the domain and range.

- $\{ ( 12,1 ) , ( - 8,7 ) , ( 10,2 ) , ( 8,5 ) \}$

A) domain $= \{ 8,10,12 , - 8 \} ;$ range $= \{ 5,5,2,1,7 \}$
B) domain $= \{ 5,2,1,7 \}$ ; range $= \{ 8,10,12 , - 8 \}$
C) domain $= \{ 8,10,12 , - 8 \}$ ; range $= \{ 5 , - 1,2,1,7 \}$
D) domain $= \{ 8,10,12 , - 8 \}$ ; range $= \{ 5,2,1,7 \}$

Question 6

Decide whether the relation is a function.
$$\{ ( - 6,5 ) , ( - 6 , - 7 ) , ( 1,2 ) , ( 6,6 ) , ( 9,8 ) \}$$

A) not a function
B) function

Question 7

Find the domain and range.
$$\{ ( 5,1 ) , ( 5 , - 4 ) , ( 6,7 ) , ( 3,4 ) , ( - 9 , - 6 ) \}$$

A) domain $= \{ 6,13 , - 9,3,5 \} ;$ range $= \{ 7 , - 6,4 , - 4,1 \}$
B) domain $= \{ 6 , - 3 , - 9,3,5 \}$ ; range $= \{ 7 , - 6,4 , - 4,1 \}$
C) domain $= \{ 6 , - 9,3,5 \}$ ; range $= \{ 7 , - 6,4 , - 4,1 \}$
D) domain $= \{ 7 , - 6,4 , - 4,1 \}$ ; range $= \{ 6,6 , - 9,3,5 \}$

Question 8

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

A) $- 1$
B) 7
C) 3
D) $- 5$

Question 9

Decide whether the relation is a function.
$$\{ ( - 8 , - 9 ) , ( - 8 , - 8 ) , ( - 1 , - 9 ) , ( 5 , - 7 ) , ( 10 , - 6 ) \}$$

A) function
B) not a function

Question 10

Find the domain and range.
$$\{ ( - 3,8 ) , ( 5,5 ) , ( - 12 , - 3 ) , ( - 11 , - 4 ) , ( 1 , - 9 ) \}$$

A) domain $= \{ 8,5,5,1 , - 9 \}$ ; range $= \{ - 11 , - 4 , - 12 , - 3 , - 3 \}$
B) domain $= \{ - 4 , - 3,8,5 , - 9 \}$ ; range $= \{ - 11 , - 12 , - 3,5,1 \}$
C) domain $= \{ - 11 , - 4 , - 12 , - 3 , - 3 \}$ ; range $= \{ 8,5,5,1 , - 9 \}$
D) domain $= \{ - 11 , - 12 , - 3,5,1 \}$ ; range $= \{ - 4 , - 3,8,5 , - 9 \}$

Question 11

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

A) function
B) not a function

Question 12

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

A) function
B) not a function

Question 13

Decide whether the relation is a function.
$$\{ ( - 2,4 ) , ( 2 , - 4 ) , ( 6 , - 6 ) , ( 9,7 ) , ( 12 , - 7 ) \}$$

A) function
B) not a function

Question 14

Decide whether the relation is a function.
$$\{ ( - 6,4 ) , ( - 1,5 ) , ( 1,1 ) , ( 1,7 ) \}$$

A) not a function
B) function

Question 15

Find the domain and range.
$$\{ ( - 4,13 ) , ( - 3,6 ) , ( 0 , - 3 ) , ( 3,6 ) , ( 5,22 ) \}$$

A) domain: $\{ 13,6 , - 3,22 \}$ ; range: $\{ - 4 , - 3,3,5 \}$
B) domain: $\{ 13,6 , - 3,22 \}$ ; range: $\{ - 4 , - 3,0,3,5 \}$
C) domain: $\{ - 4 , - 3,0,3,5 \}$ ; range: $\{ 13,6 , - 3,22 \}$
D) domain: $\{ - 4 , - 3,3,5 \}$ ; range: $\{ 13,6 , - 3,22 \}$

Question 16

Find the domain and range.
$\{ ( - 1,3 ) , ( - 3 , - 9 ) , ( 9 , - 3 ) , ( 9 , - 1 ) \}$

A) domain $= \{ - 1,9 , - 3 \}$ ; range $= \{ 3 , - 3 , - 9 , - 1 \}$
B) domain $= \{ - 1,9 , - 3 , - 9 \}$ ; range $= \{ 3 , - 3 , - 9 , - 1 \}$
C) domain $= \{ - 1,9 , - 3,19 \}$ ; range $= \{ 3 , - 3 , - 9 , - 1 \}$
D) domain $= \{ 3 , - 3 , - 9 , - 1 \}$ ; range $= \{ - 1,9 , - 3 \}$

Question 17

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

A) not a function
B) function

Question 18

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

A) domain $= \{ - 1,1,6,16 \}$ ; range $= \{ - 9,7,1 , - 6 \}$
B) domain $= \{ - 1,1,6 , - 6 \}$ ; range $= \{ - 9,7,1 , - 6 \}$
C) domain $= \{ - 9,7,1 , - 6 \}$ ; range $= \{ - 1,1,6 \}$
D) domain $= \{ - 1,1,6 \}$ ; range $= \{ - 9,7,1 , - 6 \}$

Question 19

Decide whether the relation is a function.
$$\{ ( - 5 , - 2 ) , ( - 3 , - 9 ) , ( 4 , - 3 ) , ( 4 , - 4 ) \}$$

A) function
B) not a function

Question 20

Decide whether the relation is a function.
$\{ ( 1,3 ) , ( 3 , - 6 ) , ( 5 , - 9 ) , ( 7,6 ) , ( 11,3 ) \}$

A) function
B) not a function

Question 21

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 22

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 23

Find the indicated function value.
$$\begin{array}{l}\begin{array} { c | c } x & f ( x ) \\\hline - 3 & 0 \\- 1 & 10 \\0 & 15 \\1 & 20 \\3 & 30\end{array}\\\text { Find } f ( - 1 )\end{array}$$

A) 20
B) 30
C) 10
D) 0

Question 24

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 25

Find the indicated function value.
Find f(5) when f(x) = 5.

A) 5
B) 0
C) -5
D) -25

Question 26

Find the indicated function value.
Find $f ( 0 )$ when $f ( x ) = x ^ { 2 } - 2 x + 7$

A) 49
B) 7
C) $- 7$
D) 0

Question 27

Find the indicated function value.
Find $r ( a + 4 )$ when $r ( x ) = \frac { 7 } { x + 5 }$

A) $\frac { 7 } { 5 } a + \frac { 28 } { 5 }$
B) $\frac { 11 } { a + 5 }$
C) $\frac { 7 } { a + 5 } + \frac { 7 } { 9 }$
D) $\frac { 7 } { a + 9 }$

Question 28

Find the indicated function value.
Find g(a - 1) when g(x) = 3x - 4.

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

Question 29

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 30

Find the indicated function value.
Find $f ( 3 )$ when $f ( x ) = \frac { x ^ { 2 } + 4 } { x ^ { 3 } - 6 x }$ .

A) $\frac { 13 } { 27 }$
B) $\frac { 13 } { 9 }$
C) $\frac { 13 } { 21 }$
D) 1

Question 31

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 32

Find the indicated function value.
Find $f ( 3 )$ when $f ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 2 } + 1 }$ .

A) $\frac { 3 } { 2 }$
B) $\frac { 33 } { 10 }$
C) $\frac { 11 } { 3 }$
D) $\frac { 27 } { 10 }$

Question 33

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 34

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 35

Find the indicated function value.
Find f(-9) when f(x) = -5x - 8.

A) 44.2
B) 37
C) -53
D) 53

Question 36

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 37

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 38

Find the indicated function value.
$$\begin{array}{l}\begin{array} { c | c } \mathrm { x } & \mathrm { f } ( \mathrm { x } ) \\\hline - 5 & - 6 \\- 3 & 0 \\0 & 9 \\3 & 18 \\5 & 24\end{array}\\\text { For what value of } x \text { is } f ( x ) = 9 \text { ? }\end{array}$$

A) -3
B) -5
C) 3
D) 0

Question 39

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

A) -3
B) 13
C) 11
D) 29

Question 40

Find the indicated function value.
Find $g ( a - 1 )$ when $g ( x ) = \frac { 1 } { 5 } x - 5$

A) $\frac { a + 26 } { 5 }$
B) $\frac { a - 26 } { 5 }$
C) $\frac { a - 30 } { 5 }$
D) $\frac { a - 51 } { 5 }$

Question 41

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 24%
C) approximately 25.5%
D) approximately 29%

Question 42

Express the interval in set builder notation and graph the interval on a number line.
$$( - \infty , - 6 ]$$

A) $\{ x \mid x < - 6 \}$

B) $\{ x \mid x < - 6 \}$


C) $\{ x \mid x \leq - 6 \}$

D) $\{ x \mid x \leq - 6 \}$

Question 43

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 44

Express the interval in set builder notation and graph the interval on a number line.
[-6, 8)

A) $\{ x \mid - 6 < x \leq 8 \}$

B) $\{ x \mid - 6 \leq x < 8 \}$


C) $\{ x \mid - 6 \leq x \leq 8 \}$

D) $\{ x \mid x < 8 \}$

Question 45

Express the interval in set builder notation and graph the interval on a number line.
$$( - \infty , - 8 )$$

A) $\{ x \mid x \leq - 8 \}$

B) $\{ x \mid x < - 8 \}$

C) $\{ x \mid x < - 8 \}$

D) $\{ x \mid x \leq - 8 \}$

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) = 15%, what year is represented by x?

A) 1985
B) 1990
C) 1980
D) 1995

Question 47

Express the interval in set builder notation and graph the interval on a number line.
$[ 8 , \infty )$

A) $\{ x \mid x \geq 8 \}$

B) $\{ x \mid x > 8 \}$

C) $\{ x \mid x > 8 \}$

D) $\{ x \mid x \geq 8 \}$

Question 48

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

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

Question 49

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

A) 7
B) 9
C) -9
D) 1.5

Question 50

Express the interval in set builder notation and graph the interval on a number line.
$$( - 3 , \infty )$$

A) $\{ x \mid x > - 3 \}$

B) $\{ x \mid x \geq - 3 \}$


C) $\{ x \mid x \geq - 3 \}$

D) $\{ x \mid x > - 3 \}$

Question 51

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

A) 3.5
B) 2.5
C) -0.5
D) 7

Question 52

Express the interval in set builder notation and graph the interval on a number line.
$( - 9,4 )$

A) $\{ x \mid - 9 \leq x \leq 4 \}$

B) $\{ x \mid - 9 < x < 4 \}$


C) $\{ x \mid - 9 < x \leq 4 \}$

D) $\{ x \mid - 9 \leq x < 4 \}$

Question 53

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 54

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 55

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) yes
B) no

Question 56

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 1990 and 1995
C) between 1980 and 1985
D) between 1970 and 1975

Question 57

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

A) -3
B) 3
C) 1.5
D) 9

Question 58

Express the interval in set builder notation and graph the interval on a number line.
$$[ - 9,4 ]$$

A) $\{ x \mid - 9 \leq x < 4 \}$

B) $\{ x \mid - 9 < x \leq 4 \}$


C) $\{ x \mid - 9 \leq x \leq 4 \}$

D) $\{ x \mid - 9 < x < 4 \}$

Question 59

Express the interval in set builder notation and graph the interval on a number line.
(-1, 4]

A) $\{ x \mid - 1 < x \leq 4 \}$

B) $\{ x \mid x \leq 4 \}$


C) $\{ \mathrm { x } \mid - 1 \leq \mathrm { x } \leq 4 \}$

D) $\{ x \mid - 1 < x < 4 \}$

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.
$$f ( x ) = 3 x ^ { 2 } + 3 x + 6 , g ( x ) = 4 x - 1$$
Find $( f + g ) ( - 5 )$ .

A) 165
B) 171
C) $- 105$
D) 45

Question 62

Find the domain of the function.
$$f ( x ) = \frac { 1 } { x - 6 } + \frac { 4 } { x + 12 }$$

A) $( \infty , \infty )$
B) $( \infty , - 6 )$ or $( - 6,12 )$ or $( 12 , \infty )$
C) $( \infty , - 12 )$ or $( 6 , \infty )$
D) $( \infty , - 12 )$ or $( - 12,6 )$ or $( 6 , \infty )$

Question 63

Find the domain of the function.
$$f ( x ) = x - \frac { 5 } { x + 9 }$$

A) $( \infty , \infty )$
B) $( x , 5 )$ or $( 5 , \infty )$
C) $( \infty , - 9 )$ or $( - 9 , \infty )$
D) $( \infty , 0 )$ or $( 0 , \infty )$

Question 64

Find the domain of the function.
$$f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 15 }$$

A) $( \infty , - 15 )$ or $( - 15 , \infty )$
B) $( - 15 , \infty )$
C) $( \infty , 0 )$ or $( 0 , \infty )$
D) $( \infty , \infty )$

Question 65

Express the interval in set builder notation and graph the interval on a number line.

A) domain: $[ - 2 , \infty )$
range: $( \infty , \infty )$
B) domain: $( \infty , \infty )$
range: $( - 2 , \infty )$
C) domain: $( \infty , \infty )$
range: $[ - 2 , \infty )$
D) domain: $( - 2 , \infty )$
range: $( \infty , \infty )$

Question 66

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

A) $- 3$
B) $- 11$
C) $- 17$
D) $- 9$

Question 67

Find the domain of the function.
$$f ( x ) = x ^ { 2 } + 1$$

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

Question 68

Express the interval in set builder notation and graph the interval on a number line.
$[ 2.5 , \infty )$

A) $\{ x \mid x < 2.5 \}$

B) $\{ x \mid x > 2.5 \}$

C) $\{ x \mid x \geq 2.5 \}$

D) $\{ x \mid x \leq 2.5 \}$

Question 69

Find the indicated function value.
$$f ( x ) = 5 - 8 x , g ( x ) = - 3 x + 8$$
Find $( f + g ) ( x )$ .

A) $- 5 x + 13$
B) $2 x$
C) $- 3 x + 5$
D) $- 11 x + 13$

Question 70

Find the domain of the function.
$$f ( x ) = \frac { - 2 x } { x + 3 }$$

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

Question 71

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

A) $- 33$
B) $- 23$
C) 2
D) $- 3$

Question 72

Find the domain of the function.
$$f ( x ) = - 5 x + 9$$

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

Question 73

Express the interval in set builder notation and graph the interval on a number line.
$( 3.5 , \infty )$

A) $\{ x \mid x \leq 3.5 \}$

B) $\{ x \mid x < 3.5 \}$

C) $\{ x \mid x \geq 3.5 \}$

D) $\{ x \mid x > 3.5 \}$

Question 74

Express the interval in set builder notation and graph the interval on a number line.

A) domain: $( \infty , \infty )$
range: $[0,5]$

B) domain: $[ 0,5 ]$
range: $(\infty, \infty)$

C) domain: $( \infty , \infty )$
range: $[2,5]$

D) domain: $[ 2,5 ]$
range: $(\infty, \infty)$

Question 75

Express the interval in set builder notation and graph the interval on a number line.

A) domain: $[ 4 , \infty )$
range: $( \infty , \infty )$

B) domain: $( \infty , \infty )$
range: $[ 4 , \infty )$

C) domain: $( \infty , \infty )$
range: $( 4 , \infty )$ )

D) domain: $( 4 , \infty )$ )
range: $( \infty , \infty )$

Question 76

Express the interval in set builder notation and graph the interval on a number line.

A)domain: $(0, \infty)$
range: $(\infty, \infty)$

B)domain: $(\infty, \infty)$
range: $(\infty, \infty)$

C) domain: $(\infty, \infty)$
range: $0,\infty)$

D)domain: $(0, \infty)$
range: $(0, \infty)$

Question 77

Express the interval in set builder notation and graph the interval on a number line.
$$( - \infty , 6.5 )$$

A) $\{ x \mid x \leq 6.5 \}$

B) $\{ x \mid x \geq 6.5 \}$


C) $\{ x \mid x < 6.5 \}$

D) $\{ x \mid x > 6.5 \}$

Question 78

Express the interval in set builder notation and graph the interval on a number line.

A) domain: $( * , \infty )$
range: $\{-2\}$

B) domain: $( 0 , \infty )$
range: $\{-2\}$

C) domain: $\{ - 2 \}$
range: $(0, \infty)$

D) domain: $\{ - 2 \}$
range: $(*, \infty)$

Question 79

Express the interval in set builder notation and graph the interval on a number line.
$$( - \infty , 4.5 \text { ] }$$

A) $\{ x \mid x < 4.5 \}$

B) $\{ x \mid x \leq 4.5 \}$


C) $\{ x \mid x \geq 4.5 \}$

D) $\{ x \mid x > 4.5 \}$

Question 80

Find the domain of the function.
$$f ( x ) = \frac { 1 } { x - 8 }$$

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