Deck 2: Functions and Graphs

Question 1

Determine whether the equation defines y as a function of x.
x2 + y = 25

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

Answer 1

A

Question 2

Give the domain and range of the relation.
{(6, 6), (11, -5), (3, 4), (3, -3)}

A)domain = {6, 3, 11}; range = {6, 4, -5, -3}
B)domain = {6, 3, 11, -3}; range = {6, 4, -5, -3}
C)domain = {6, 3, 11, 13}; range = {6, 4, -5, -3}
D)domain = {6, 4, -5, -3}; range = {6, 3, 11}

Answer 2

A

Question 3

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

A)Not a function
B)Function

Answer 3

A

Question 4

Give the domain and range of the relation.
{(-5, 1), (-5, 3), (9, 9), (4, -4), (-1, -1)}

A)domain = {4, -5, -1, 9}; range = {-4, 3, -1, 9, 1}
B)domain = {4, -4, -5, -1, 9}; range = {-4, 3, -1, 9, 1}
C)domain = {4, 14, -5, -1, 9}; range = {-4, 3, -1, 9, 1}
D)domain = {-4, 3, -1, 9, 1}; range = {4, 4, -5, -1, 9}

Question 5

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

A)Not a function
B)Function

Question 6

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

A)Not a function
B)Function

Question 7

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

A)Function
B)Not a function

Question 8

Give the domain and range of the relation.
{(1, -7), (7, 1), (3, -1), (3, 4)}

A)domain = {1, 3, 7}; range = {-7, -1, 1, 4}
B)domain = {-7, -1, 1, 4}; range = {1, 3, 7}
C)domain = {1, 3, 7, 13}; range = {-7, -1, 1, 4}
D)domain = {1, 3, 7, -3}; range = {-7, -1, 1, 4}

Question 9

Determine whether the relation is a function.
{(1, -2), (1, -4), (4, -3), (9, -1), (12, 5)}

A)Not a function
B)Function

Question 10

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

A)Function
B)Not a function

Question 11

Give the domain and range of the relation.
{(-4, -5), (9, -1), (7, 3), (-3, -3)}

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

Question 12

Determine whether the relation is a function.
{(-7, -1), (-3, -6), (-2, -7), (2, -2)}

A)Function
B)Not a function

Question 13

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

A)Not a function
B)Function

Question 14

Determine whether the relation is a function.
{(-3, -8), (3, 6), (5, -5), (7, -6), (10, 6)}

A)Function
B)Not a function

Question 15

Determine whether the equation defines y as a function of x.
x + y = 49

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

Question 16

Determine whether the equation defines y as a function of x.
5x + 7y = 8

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

Question 17

Give the domain and range of the relation.
{(6, -5), (3, 2), (4, 6), (-1, 3), (-4, 9)}

A)domain = {4, -1, 3, 6, -4}; range = {6, 3, 2, -5, 9}
B)domain = {6, 3, 2, -5, 9}; range = {4, -1, 3, 6, -4}
C)domain = {4, 6, -1, 3, 3}; range = {2, 6, -5, -4, 9}
D)domain = {2, 6, -5, -4, 9}; range = {4, 6, -1, 3, 3}

Question 18

Determine whether the relation is a function.
{(-1, -6), (2, -5), (4, 9), (8, -5), (10, 3)}

A)Function
B)Not a function

Question 19

Give the domain and range of the relation.
{(41, -3), (5, -2), (5, 0), (9, 2), (21, 4)}

A)domain: {41, 9, 5, 21}; range: {-3, -2, 0, 2, 4}
B)domain: {-3, -2, 2, 4}; range: {41, 9, 5, 21}
C)domain: {-3, -2, 0, 2, 4}; range: {41, 9, 5, 21}
D)domain: {41, 9, 5, 21}; range: {-3, -2, 2, 4}

Question 20

Give the domain and range of the relation.
{(-2, 6), (-1, 3), (0, 2), (1, 3), (3, 11)}

A)domain: {-2, -1, 0, 1, 3}; range: {6, 3, 2, 11}
B)domain: {-2, -1, 1, 3}; range: {6, 3, 2, 11}
C)domain: {6, 3, 2, 11}; range: {-2, -1, 0, 1, 3}
D)domain: {6, 3, 2, 11}; range: {-2, -1, 1, 3}

Question 21

Evaluate a Function
Evaluate the function at the given value of the independent variable and simplify.
$$h ( x ) = | x - 11 | ; \quad h ( 15 )$$

A) 4
В) $- 26$
C) 26
D) $- 4$

Question 22

Evaluate a Function
Evaluate the function at the given value of the independent variable and simplify.
$$f ( x ) = \sqrt { x + 19 } ; \quad f ( - 3 )$$

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

Question 23

Determine whether the equation defines y as a function of x.
$$x ^ { 2 } + y ^ { 2 } = 36$$

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.
$$y = \sqrt { 6 x - 2 }$$

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

Question 25

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 26

Evaluate a Function
Evaluate the function at the given value of the independent variable and simplify.
$f ( x ) = 3 x ^ { 2 } - 4 x + 2 ; \quad f ( x - 1 )$

A) $3 x ^ { 2 } - 10 x + 9$
B) $- 10 x ^ { 2 } + 3 x + 9$
C) $3 x ^ { 2 } - 10 x + 1$
D) $3 x ^ { 2 } + 2 x + 1$

Question 27

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 28

Evaluate a Function
Evaluate the function at the given value of the independent variable and simplify.
$$f ( x ) = \frac { x ^ { 3 } + 8 } { x ^ { 2 } - 4 } ; \quad f ( 5 )$$

A) $\frac { 19 } { 3 }$
B) $\frac { 133 } { 25 }$
C) $\frac { 125 } { 21 }$
D) $\frac { 11 } { 7 }$

Question 29

Determine whether the equation defines y as a function of x.
$$| x | - y = 6$$

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

Question 30

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

A) $- \frac { 1 } { 4 }$
B) $\frac { 1 } { 8 }$
C) $\frac { 1 } { 2 }$
D) - 1

Question 31

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

A) $x ^ { 2 } + 6 x + 5$
B) $x ^ { 2 } + 9$
C) $x ^ { 2 } + 6 x + 9$
D) $x ^ { 2 } - 1$

Question 32

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 33

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 34

Evaluate a Function
Evaluate the function at the given value of the independent variable and simplify.
$$g ( x ) = 3 x + 1 ; \quad g ( x + 1 )$$

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

Question 35

Solve the problem.
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)= 0.3x + 27,000. Find C(90,000), the cost of producing 90,000 jars.

A)$54,000
B)$27,000
C)$27.30
D)$90,027

Question 36

Determine whether the equation defines y as a function of x.
$$x + y ^ { 2 } = 1$$

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

Question 37

Determine whether the equation defines y as a function of x.
$$y = - \sqrt { x - 8 }$$

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

Question 38

Solve the problem.
The function P(x)= 0.65x - 57 models the relationship between the number of pretzels x that a certain vendor sells and the profit the vendor makes. Find P(1000), the profit the vendor makes from selling 1000
Pretzels.

A)$593
B)$650
C)$707
D)$943

Question 39

Determine whether the equation defines y as a function of x.
$$y ^ { 2 } = 6 x$$

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

Question 40

Evaluate a Function
Evaluate the function at the given value of the independent variable and simplify.
$f ( x ) = 2 x + 4 ; \quad f ( 6 )$

A) 16
B) 36
C) 8
D) 6

Question 41

Use the Vertical Line Test to Identify Functions
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 42

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

$\text { A) not a function }$

B) function

Question 43

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

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 44

Graph Functions by Plotting Points
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 45

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

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 46

Use the Vertical Line Test to Identify Functions
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 47

Graph Functions by Plotting Points
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 $f$ vertically down 1 unit

B) $g$ shifts the graph of $f$ vertically up 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 48

Graph Functions by Plotting Points
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 49

Graph Functions by Plotting Points
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 up 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 50

Use the Vertical Line Test to Identify Functions
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 51

Graph Functions by Plotting Points
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 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 52

Graph Functions by Plotting Points
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 53

Use the Vertical Line Test to Identify Functions
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 54

Use the Vertical Line Test to Identify Functions
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 55

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

Question 56

Use the Vertical Line Test to Identify Functions
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 57

Graph Functions by Plotting Points
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 58

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

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 down 3 units

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

Question 59

Graph Functions by Plotting Points
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
graph of f.
$f(x)=x^{2}, g(x)=x^{2}+1$

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 60

Graph Functions by Plotting Points
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 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. $$\text { Percent of Students in College of Engineering }$$

A) domain: $( - \infty , \infty )$
range: $( - \infty , 4 ]$
B) domain: $( - \infty , \infty )$
range: $( - \infty , \infty )$
C) domain: $( - \infty , 5 ]$
range: $( - \infty , 4 ]$
D) domain: $( - \infty , 5 )$ or $( 5 , \infty )$
range: $( - \infty , 4 )$ or $( 4 , \infty )$

Question 62

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

A) domain: $( - \infty , \infty )$
range:([ 0,4 ]
B) domain: $( - \infty , \infty )$
range: $[ 2,4 ]$
C) domain: $[ 0,4 ]$
range: $( - \infty , \infty )$
D) domain: $[ 2,4 ]$ )
range: $( - \infty , \infty )$

Question 63

Identify the intercepts.

A) $( 2,0 ) , ( 0,6 )$
B) $( - 2,0 ) , ( 0,6 )$
C) $( 2,0 ) , ( 0 , - 6 )$
D) $( - 6,0 ) , ( 0,6 )$

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. $$\text { Percent of Students in College of Engineering }$$


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 8 Identify the Domain and Range of a Function from Its Graph

Question 65

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(1990).

A)approximately 26%
B)approximately 28%
C)approximately 22.5%
D)approximately 21%

Question 66

Use the Vertical Line Test to Identify Functions
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 67

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

A) domain: $[ 0 , \infty )$
range: $[ - 2 , \infty )$
B) domain: $[ 0 , \infty )$
range: $( - \infty , \infty )$
C) domain: $( - \infty , \infty )$
range: $[ - 2 , \infty )$
D) domain: $[ 0 , \infty )$
range: $[ 0 , \infty )$

Question 68

Use the Vertical Line Test to Identify Functions
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 69

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

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

Question 70

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 71

Identify the intercepts.

A) $( 1,0 ) , ( 0 , - 7 )$
B) $( - 1,0 ) , ( 0 , - 7 )$
C) $( 1,0 ) , ( 0,7 )$
D) $( - 7,0 ) , ( 0,7 )$

Question 72

Identify the intercepts.

A) $( - 2,0 ) , ( 0,6 )$
B) $( 2,0 ) , ( 0,6 )$
C) $( - 2,0 ) , ( 0 , - 6 )$
D) $( - 6,0 ) , ( 0,6 )$

Question 73

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

A) 2
B) $- 2$
C) 5
D) $1.25$

Question 74

Use the graph to find the indicated function value.
y = f(x). Find f(-1)

A) $2.5$
B) $- 2.5$
C) $0.3$
D) $- 0.3$

Question 75

Use the Vertical Line Test to Identify Functions
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 76

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)= 26%, what year is represented by x?

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

Question 77

Use the Vertical Line Test to Identify Functions
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 78

Use the Vertical Line Test to Identify Functions
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 79

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

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

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. $$\text { Percent of Students in College of Engineering }$$


Does the graph represent a function?

A)yes
B)no