Deck 2: Functions and Graphs

Question 1

Determine whether the relation is a function.
$$\{ ( - 6 , - 9 ) , ( - 4 , - 8 ) , ( 1,6 ) , ( 3 , - 9 ) \}$$

A) Function
B) Not a function

Answer 1

A

Question 2

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

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

Answer 2

A

Question 3

Determine whether the relation is a function.
$$\{ ( - 3,7 ) , ( 2 , - 9 ) , ( 4,1 ) , ( 8,5 ) , ( 11 , - 1 ) \}$$

A) Function
B) Not a function

Answer 3

A

Question 4

Give the domain and range of the relation.
$$\{ ( - 12,8 ) , ( - 12 , - 5 ) , ( - 3,2 ) , ( - 10 , - 8 ) , ( 6,3 ) \}$$

A) domain $= \{ - 10,6 , - 12 , - 3 \}$ ; range $= \{ - 8,3 , - 5,2,8 \}$
B) domain $= \{ - 10 , - 4,6 , - 12 , - 3 \}$ ; range $= \{ - 8,3 , - 5,2,8 \}$
C) domain $= \{ - 10,14,6 , - 12 , - 3 \} ;$ range $= \{ - 8,3 , - 5,2,8 \}$
D) domain $= \{ - 8,3 , - 5,2,8 \}$ ; range $= \{ - 10 , - 10,6 , - 12 , - 3 \}$

Question 5

Give the domain and range of the relation.
$$\{ ( - 4 , - 8 ) , ( - 12,8 ) , ( - 10,1 ) , ( 3 , - 3 ) , ( 4,9 ) \}$$

A) domain $= \{ 4 , - 12,3 , - 4 , - 10 \} ;$ range $= \{ 9,8 , - 3 , - 8,1 \}$
B) domain $= \{ 9,8 , - 3 , - 8,1 \} ;$ range $= \{ 4 , - 12,3 , - 4 , - 10 \}$
C) domain $= \{ 4,9 , - 12,8,3 \}$ ; range $= \{ - 3 , - 4 , - 8 , - 10,1 \}$
D) domain $= \{ - 3 , - 4 , - 8 , - 10,1 \} ;$ range $= \{ 4,9 , - 12,8,3 \}$

Question 6

Give the domain and range of the relation.
$$\{ ( 4,4 ) , ( - 9,8 ) , ( 7,1 ) , ( - 7 , - 5 ) \}$$

A) domain $= \{ - 7,4,7 , - 9 \}$ ; range $= \{ - 5,4,1,8 \}$
B) domain $= \{ - 5,4,1,8 \}$ ; range $= \{ - 7,4,7 , - 9 \}$
C) domain $= \{ - 7,4,7 , - 9 \}$ ; range $= \{ - 5 , - 4,4,1,8 \}$
D) domain $= \{ - 7,4,7 , - 9 \}$ ; range $= \{ - 5 , - 5,4,1,8 \}$

Question 7

Give the domain and range of the relation.
$\{ ( - 2 , - 8 ) , ( 12,5 ) , ( 2,1 ) , ( 2 , - 5 ) \}$

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

Question 8

Determine whether the equation defines y as a function of x.
$$x ^ { 2 } + y = 4$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 9

Determine whether the relation is a function.
$$\{ ( 3 , - 1 ) , ( 3,8 ) , ( 5 , - 6 ) , ( 7,3 ) , ( 11 , - 2 ) \}$$

A) Not a function
B) Function

Question 10

Determine whether the relation is a function.
$$\{ ( - 4,1 ) , ( - 1 , - 9 ) , ( 1 , - 3 ) , ( 5 , - 6 ) \}$$

A) Function
B) Not a function

Question 11

Determine whether the relation is a function.
$$\{ ( - 6 , - 3 ) , ( - 2,3 ) , ( - 1 , - 8 ) , ( - 1,8 ) \}$$

A) Not a function
B) Function

Question 12

Determine whether the equation defines y as a function of x.
$$6 x + 6 y = 11$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 13

Give the domain and range of the relation.
$$\{ ( - 1 , - 4 ) , ( - 2 , - 3 ) , ( - 2,0 ) , ( 7,3 ) , ( 23,5 ) \}$$

A) domain: $\{ - 1,7 , - 2,23 \}$ ; range: $\{ - 4 , - 3,0,3,5 \}$
B) domain: $\{ - 4 , - 3,3,5 \}$ ; range: $\{ - 1,7 , - 2,23 \}$
C) domain: $\{ - 4 , - 3,0,3,5 \}$ ; range: $\{ - 1,7 , - 2,23 \}$
D) domain: $\{ - 1,7 , - 2,23 \}$ ; range: $\{ - 4 , - 3,3,5 \}$

Question 14

Give the domain and range of the relation.
$$\{ ( - 5 , - 5 ) , ( - 2 , - 6 ) , ( 12,7 ) , ( 12 , - 8 ) \}$$

A) domain $= \{ - 5,12 , - 2 \} ;$ range $= \{ - 5,7 , - 6 , - 8 \}$
B) domain $= \{ - 5,7 , - 6 , - 8 \}$ ; range $= \{ - 5,12 , - 2 \}$
C) domain $= \{ - 5,12 , - 2,22 \}$ ; range $= \{ - 5,7 , - 6 , - 8 \}$
D) domain $= \{ - 5,12 , - 2 , - 12 \}$ ; range $= \{ - 5,7 , - 6 , - 8 \}$

Question 15

Determine whether the relation is a function.
$$\{ ( - 9,9 ) , ( - 9 , - 1 ) , ( 2 , - 8 ) , ( 5,4 ) , ( 10 , - 9 ) \}$$

A) Not a function
B) Function

Question 16

Determine whether the equation defines y as a function of x.
$$x + y = 81$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 17

Determine whether the relation is a function.
$$\{ ( - 3,2 ) , ( 3 , - 1 ) , ( 4,7 ) , ( 7 , - 5 ) , ( 11,4 ) \}$$

A) Function
B) Not a function

Question 18

Determine whether the relation is a function.
$$\{ ( - 9,5 ) , ( - 9 , - 4 ) , ( 1 , - 6 ) , ( 5 , - 5 ) , ( 8 , - 2 ) \}$$

A) Not a function
B) Function

Question 19

Determine whether the relation is a function.
$$\{ ( - 5,3 ) , ( - 2 , - 2 ) , ( 4,5 ) , ( 8,9 ) \}$$

A) Function
B) Not a function

Question 20

Determine whether the relation is a function.
$$\{ ( - 6,3 ) , ( - 1 , - 1 ) , ( 3 , - 1 ) , ( 3 , - 2 ) \}$$

A) Not a function
B) Function

Question 21

Determine whether the equation defines y as a function of x.
$$y = - \sqrt { x + 6 }$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 22

Evaluate the function at the given value of the independent variable and simplify.
$$f ( x ) = \frac { x ^ { 2 } - 7 } { x ^ { 3 } - 2 x } ; f ( 4 )$$

A) $\frac { 9 } { 56 }$
B) $\frac { 9 } { 64 }$
C) $\frac { 9 } { 62 }$
D) $\frac { 2 } { 7 }$

Question 23

Determine whether the equation defines y as a function of x.
$$| x | - y = 2$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 24

Determine whether the equation defines y as a function of x.
$$x ^ { 2 } + y ^ { 2 } = 16$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 25

Evaluate the function at the given value of the independent variable and simplify.
$h ( x ) = | x - 3 | ; \quad h ( 16 )$

A) 13
В) $- 19$
C) 19
D) $- 13$

Question 26

Determine whether the equation defines y as a function of x.
$$y = \sqrt { - 6 x + 5 }$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 27

Determine whether the equation defines y as a function of x.
$$x = y ^ { 2 }$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 28

Evaluate the function at the given value of the independent variable and simplify.
$$f ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 2 } + 4 } ; \quad f ( 4 )$$

A) $\frac { 7 } { 2 }$
B) $\frac { 35 } { 8 }$
C) $\frac { 16 } { 5 }$
D) $\frac { 11 } { 10 }$

Question 29

Determine whether the equation defines y as a function of x.
$$y = x ^ { 3 }$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 30

Determine whether the equation defines y as a function of x.
$$y ^ { 2 } = 3 x$$

A) $y$ is a function of $x$
B) $y$ is not $a$ function of $x$

Question 31

Evaluate the function at the given value of the independent variable and simplify.
$$f ( x ) = x ^ { 2 } + 3 ; \quad f ( x + 4 )$$

A) $x ^ { 2 } + 8 x + 19$
B) $x ^ { 2 } + 16$
C) $x ^ { 2 } + 8 x + 16$
D) $x ^ { 2 } + 7$

Question 32

Evaluate the function at the given value of the independent variable and simplify.
The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the function $C ( x ) = 0.5 x + 20,000$ . Find $C ( 50,000 )$ , the cost of producing 50,000 jars.

A) $\$ 45,000$
B) $\$ 25,000$
C) $\$ 20.50$
D) $\$ 50,020$

Question 33

Evaluate the function at the given value of the independent variable and simplify.
$f ( x ) = \sqrt { x + 20 } ; \quad f ( - 4 )$

A) 4
В) $- 4$
C) 2
D) not a real number

Question 34

Evaluate the function at the given value of the independent variable and simplify.
$$f ( x ) = - 6 x - 5 ; \quad f ( - 3 )$$

A) 13
B) 33
C) 23
D) $- 11$

Question 35

Determine whether the equation defines y as a function of x.
$$x y + 6 y = 1$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 36

Evaluate the function at the given value of the independent variable and simplify.
$$f ( x ) = 3 x ^ { 2 } - 3 x - 5 ; \quad f ( x - 1 )$$

A) $3 x ^ { 2 } - 9 x + 1$
B) $- 9 x ^ { 2 } + 3 x + 1$
C) $3 x ^ { 2 } - 9 x - 5$
D) $3 x ^ { 2 } - 18 x - 5$

Question 37

Evaluate the function at the given value of the independent variable and simplify.
The function $P ( x ) = 0.6 x - 89$ models the relationship between the number of pretzels $x$ that a certain vendor sells and the profit the vendor makes. Find $\mathrm { P } ( 500 )$ , the profit the vendor makes from selling 500 pretzels.

A) \$211
B) $\$ 300$
C) $\$ 389$
D) $\$ 411$

Question 38

Evaluate the function at the given value of the independent variable and simplify.
$$g ( x ) = 2 x + 4 ; \quad g ( x - 1 )$$

A) $2 x + 2$
B) $2 x + 4$
C) $2 x + 1$
D) $\frac { 1 } { 2 } x + 4$

Question 39

Determine whether the equation defines y as a function of x.
$$x + y ^ { 3 } = 1$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 40

Determine whether the equation defines y as a function of x.
$$x + y ^ { 2 } = 49$$

A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Question 41

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$(x)=\sqrt{x}, g(x)=\sqrt{x}-3$

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 down 3 units

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

Question 42

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

A) function
B) not a function

Question 43

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

A) not a function
B) function

Question 44

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=|x|, g(x)=|x|+1$

A) $g$ shifts the graph of $f$ vertically up 1 unit

B) $g$ shifts the graph of $f$ vertically down 1 unit

C) g shifts the graph of $f$ vertically down 1 unit

D) $g$ shifts the graph of $f$ vertically up 1 unit

Question 45

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

A) $\text { not a function }$

B) function

Question 46

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=x^{2}, g(x)=x^{2}+4$

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 down 4 units

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

Question 47

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

A) function
B) not a function

Question 48

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=x^{3}, g(x)=x^{3}+3$

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

Question 49

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=-4 x, g(x)=-4 x-2$

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

Question 50

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=x, g(x)=x-4$

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 51

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

A) $\text { not a function }$
B) function

Question 52

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

A) function
B) not a function

Question 53

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=2 x^{2}, g(x)=2 x^{2}-4$

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 54

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=\sqrt{x}, g(x)=\sqrt{x+1}$

A) $g$ shifts the graph of $f 1$ unit to the left

B) $g$ shifts the graph of $f 1$ unit to the right

C) g shifts the graph of f vertically up 1 unit

D) g shifts the graph of $f$ vertically down 1 unit

Question 55

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=\sqrt{x}, g(x)=\sqrt{x}+4$

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 down 4 units

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

Question 56

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=x, g(x)=x+2$

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 down 2 units

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

Question 57

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=|x|, g(x)=|x|-2$

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

Question 58

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=\sqrt{x}, g(x)=\sqrt{x-1}$

A) $g$ shifts the graph of $f 1$ unit to the right

B) $g$ shifts the graph of $f 1$ unit to the left

C) g shifts the graph of f vertically up 1 unit

D) $g$ shifts the graph of $f$ vertically down 1 unit

Question 59

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

A) function
B) not a function

Question 60

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

A) function
B) not a function

Question 61

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use
the graph to answer the question. $$\text { Percent of Students in College of Engineering }$$


Does the graph represent a function?

A) yes
B) no

Question 62

Use the graph to find the indicated function value.
$y = f ( x ) .$ Find $f ( 2 )$

A) $- 2.7$
B) $2.7$
C) $- 0.7$
D) $0.7$

Question 63

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use
the graph to answer the question. $$\text { Percent of Students in College of Engineering }$$


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

A) between 1980 and 1985
B) between 1985 and 1990
C) between 1970 and 1975
D) between 1960 and 1965

Question 64

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use
the graph to answer the question. $$\text { Percent of Students in College of Engineering }$$


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

A) 1980
B) 1975
C) 1985
D) 1970

Question 65

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

A) function
B) not a function

Question 66

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

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

Question 67

Identify the intercepts.

A) $( - 3,0 ) , ( 0,6 )$
B) $( 3,0 ) , ( 0,6 )$
C) $( - 3,0 ) , ( 0 , - 6 )$
D) $( - 6,0 ) , ( 0,6 )$

Question 68

Identify the Domain and Range of a Function from Its Graph
Use the graph to determine the function's domain and range.

A) domain: $( - \infty , \infty )$
range: $( - \infty , 3 ]$
B) domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$
C) domain: $( - \infty , 5 ]$
range: $( - \infty , 3 ]$
D) domain: $( - \infty , 5 )$ or $( 5 , \infty )$
range: $( - \infty , 3 )$ or $( 3 , \infty )$

Question 69

Identify the Domain and Range of a Function from Its Graph
Use the graph to determine the function's domain and range.

A) domain: $[ 0 , \infty )$
range: $[ - 1 , \infty )$
B) domain: $[ 0 , \infty )$
range: $( - \infty , \infty )$
C) domain: $( - \infty , \infty )$
range: $[ - 1 , \infty )$
D) domain: $[ 0 , \infty )$
range: $[ 0 , \infty )$

Question 70

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

A) not a function
B) function

Question 71

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

A) function
B) not a function

Question 72

Identify the Domain and Range of a Function from Its Graph
Use the graph to determine the function's domain and range.

A) domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$
B) domain: $( - \infty , \infty )$
range: $\mathrm { y } = 1$
C) domain: $x = \frac { 1 } { 2 }$
range: $( - \infty , \infty )$
D) domain: $x = \frac { 1 } { 2 }$
range: $y = 1$

Question 73

Identify the Domain and Range of a Function from Its Graph
Use the graph to determine the function's domain and range.

A) domain: $( - \infty , \infty )$
range: $[ 0,5 ]$
B) domain: $( - \infty , \infty )$
range: $[ 3,5 ]$
C) domain: $[ 0,5 ]$
range: $( - \infty , \infty )$
D) domain: $[ 3,5 ]$
range: $( - \infty , \infty )$

Question 74

Identify the Domain and Range of a Function from Its Graph
Use the graph to determine the function's domain and range.

A) domain: $( - \infty , \infty )$
range: $[ - 1 , \infty )$
B) domain: $[ - 2 , \infty )$
range: $[ - 1 , \infty )$
C) domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$
D) domain: $( - \infty , - 2 )$ or $( - 2 , \infty )$
range: $( - \infty , - 1 )$ or $( - 1 , \infty )$

Question 75

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

A) function
B) not a function

Question 76

Use the graph to find the indicated function value.
$y = f ( x )$ . Find $f ( - 2 )$

A) 2
В) $- 2$
C) 5
D) $1.25$

Question 77

Use the graph to find the indicated function value.
$y = f ( x )$ . Find $f ( 5 )$

A) 11
B) 9
C) $- 11$
D) 2

Question 78

Use the graph to find the indicated function value.
$$y = f ( x ) \text {. Find } f ( - 4 )$$

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

Question 79

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

A) not a function
B) function

Question 80

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use
the graph to answer the question. $$\text { Percent of Students in College of Engineering }$$


If f represents the function, find f(1980).

A) approximately 15%
B) approximately 17%
C) approximately 11.5%
D) approximately 10%