Deck 7: Graphs, Functions, and Applications

Question 1

Is the following correspondence a function?

- $\begin{array} { r | r } \text { Name } & \text { Test Score } \\\hline \text { Bob L. } & 93 \\\hline \text { Susan H. } & 83 \\\hline \text { Jim H. } & 76 \\\hline \text { Bruce B. } & 96\end{array}$

Answer 1

True

Question 2

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

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

Answer 2

A

Question 3

Is the following correspondence a function?

-Domain: All students attending the University of Ohio Correspondence: Each student's teachers
Range: A set of teachers

Answer 3

False

Question 4

Find the function value.
Find $f ( 2 )$ when $f ( x ) = - x + 5$ .

A) $- 3$
B) 6
C) 3
D) 2

Question 5

Is the following correspondence a function?

-Domain: All students attending Laughlin Community College Correspondence: Each student's Social Security Number
Range: A set of Social Security Numbers

Question 6

Find the function value.
Find $f ( 0 )$ when $f ( x ) = x ^ { 2 } + 3 x - 3$

A) 3
B) 9
C) $- 3$
D) 0

Question 7

Find the function value.
Find $f ( 10 )$ when $f ( x ) = 9$ .

A) 9
В) $- 9$
C) 90
D) 10

Question 8

Find the function value.
Find $f ( 2 a )$ when $f ( x ) = 3 x ^ { 2 } + 6 x$ .

A) $12 a ^ { 2 } + 6 a$
B) $6 a ^ { 2 } + 12 a$
C) $3 a ^ { 2 } + 12 a$
D) $12 a ^ { 2 } + 12 a$

Question 9

Is the following correspondence a function?

-

Question 10

Is the following correspondence a function?

-

Question 11

Is the following correspondence a function?

-

Question 12

Find the function value.
Find $f ( - 4 )$ when $f ( x ) = 5 x - 1$ .

A) $- 21$
B) 21
C) $- 11$
D) $- 24$

Question 13

Find the function value.
Find $f ( 6 )$ when $f ( x ) = | x + 4 |$ .

A) $- 4$
B) 10
C) $- 10$
D) 6

Question 14

Is the following correspondence a function?

-

Question 15

Find the function value.
Find $f ( 2 )$ when $f ( x ) = 2 x ^ { 2 } + 3 x - 5$ .

A) 5
B) $- 3$
C) 19
D) 9

Question 16

Find the function value.
Find $f ( 4 )$ when $f ( x ) = - 4 x + 13$ .

A) $- 3$
B) 8
C) $- 52$
D) 13

Question 17

Is the following correspondence a function?

-

Question 18

Is the following correspondence a function?

-

Question 19

Is the following correspondence a function?

-

Question 20

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

A) $- 3$
B) 9
C) 11
D) $- 1$

Question 21

Solve the problem.
It has been determined that the number of fish $\mathrm { f } ( \mathrm { t } )$ that can be caught in $\mathrm { t }$ minutes in a certain pond using a certain bait is $f ( t ) = .28 t + 1$ , for $t > 10$ . Find the approximate number of fish that can be caught if you fish for 32 minutes.

A) About 9 fish
B) About 21 fish
C) About 36 fish
D) About 34 fish

Question 22

Graph the function.
$f(x)=x^{3}-3$

A)

B)

C)

D)

Question 23

Solve the problem.
The function $\mathrm { P } ( \mathrm { d } ) = 1 + \frac { \mathrm { d } } { 33 }$ gives the pressure, in atmospheres (atm), at a depth $\mathrm { d }$ feet in the sea. Find the pressure at 30 feet.

A) $\frac { 21 } { 11 } \mathrm {~atm}$
B) $\frac { 1 } { 11 } a t m$
C) $\frac { 10 } { 11 }$ atm
D) $\frac { 31 } { 33 } \mathrm {~atm}$

Question 24

Solve the problem.
The function $\mathrm { F }$ described by $\mathrm { F } ( \mathrm { C } ) = \frac { 9 } { 5 } \mathrm { C } + 32$ gives the Fahrenheit temperature corresponding to the Celsius temperature $\mathrm { C }$ . Find the Fahrenheit temperature equivalent to $20 ^ { \circ } \mathrm { C }$ .

A) $104 ^ { \circ } \mathrm { F }$
B) $140 ^ { \circ } \mathrm { F }$
C) $68 ^ { \circ } \mathrm { F }$
D) $176 ^ { \circ } \mathrm { F }$

Question 25

Graph the function.
$f(x)=|x|-2$

A)

B)

C)

D)

Question 26

Graph the function.
$f(x)=x^{2}+2 x-4$

A)

B)

C)

D)

Question 27

Graph the function.
$f(x)=|6-x|$

A)

B)

C)

D)

Question 28

Determine whether the graph is the graph of a function.

-

Question 29

Find the function value.
Find $f ( 10 )$ when $f ( x ) = x ^ { 3 }$ .

A) 729
B) 1000
C) 30
D) 59,049

Question 30

Graph the function.
$f(x)=-x^{2}-2 x+1$

A)

B)

C)

D)

Question 31

Determine whether the graph is the graph of a function.

-

Question 32

Graph the function.
$y=-4 x-5$

A)

B)

C)

D)

Question 33

Determine whether the graph is the graph of a function.

-

Question 34

Determine whether the graph is the graph of a function.

-

Question 35

Graph the function.
$f(x)=7-x^{2}$

A)

B)

C)

D)

Question 36

Graph the function.
$f(x)=3 x+2$

A)

B)

C)

D)

Question 37

Graph the function.
$$f ( x ) = \frac { 1 } { 4 } x + 4$$

A)

B)

C)

D)

Question 38

Determine whether the graph is the graph of a function.

-

Question 39

Find the function value.
Find $f ( - 3 )$ when $f ( x ) = x ^ { 4 } + - 3$ .

A) 24
B) 9
C) 78
D) $- 84$

Question 40

Graph the function.
$f(x)=x^{2}-2$

A)

B)

C)

D)

Question 41

The graph of a function f is provided. Determine the requested function value.
$f(-1)$

A) 0
B) $- 1$
C) $- 2$
D) 2

Question 42

For the function represented in the graph, determine the domain or range, as requested.
Find the range.

A) $\{ x \mid - 1 \leq x \leq 1 \}$
B) $\{ x \mid - 2.73 \leq x \leq 0.73 \}$
C) $\{ x \mid - 5 \leq x \leq 5 \}$
D) $\{ x \mid - 4 \leq x \leq - 1 \}$

Question 43

For the function represented in the graph, determine the domain or range, as requested.
Find the range.

A) $\{ - 4 , - 3 , - 2 , - 1,0,1,2,3,4 \}$
B) $\{ x \mid - 5 \leq x \leq 3 \}$
C) $\{ x \mid - 3 \leq x \leq 3 \}$
D) $\{ - 5 , - 4 , - 3 , - 2 , - 1,0,1,2,3 \}$

Question 44

For the function represented in the graph, determine the domain or range, as requested.
Find the domain.

A) $\{ x \mid - 5 \leq x \leq 5 \}$
B) $\{ x \mid - 5 < x < 5 \}$
C) $\{ x \mid - 4 \leq x \leq 4 \}$
D) $\{ x \mid - 5 \leq x < 5 \}$

Question 45

The graph of a function f is provided. Determine the requested function value.
$\mathrm { f } ( 1 )$

A) 1
B) $- 3$
C) $- 1$
D) $- 27$

Question 46

For the function represented in the graph, determine the domain or range, as requested.
Find the domain.

A) $\{ x \mid - 4 \leq x \leq 3 \}$
B) $\{ x \mid 0 \leq x \leq 0 \}$
C) $\{ x \mid - 5 \leq x \leq 5 \}$
D) $\{ x \mid - 5 \leq x \leq 4 \}$

Question 47

For the function represented in the graph, determine the domain or range, as requested.
Find the range.

A) $\{ x \mid - 5 \leq x \leq 5 \}$
B) $\{ x \mid - 3 \leq x \leq 5 \}$
C) $\{ - 3 , - 2 , - 1,0,1,2,3,4,5 \}$
D) $\{ x \mid - 5 \leq x \leq 3 \}$

Question 48

The graph of a function f is provided. Determine the requested function value.
$$f ( - 1 )$$

A) 4
В) $- 2$
C) 6
D) 0

Question 49

Solve.
Cars sold


Year Crafty Bill's Cool Car Sales opened as a used car sales lot in 1991. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 1995?

A)250 cars
B)850 cars
C)800 cars
D)600 cars

Question 50

Determine whether the graph is the graph of a function.

-

Question 51

Solve.
Cars sold
$$\text { Year }$$ Crafty Bill's Cool Car Sales opened as a used car sales lot in 1991. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 1993?

A)150 cars
B)600 cars
C)750 cars
D)700 cars

Question 52

For the function represented in the graph, determine the domain or range, as requested.
Find the domain.

A) $\{ x \mid - 18 \leq x \leq 18 \}$
B) $| x | - 3 \leq x \leq 3 \}$
C) $| x | - 5 \leq x \leq 5 \}$
D) all real numbers

Question 53

Solve.
The graph shows the relationship between the area A of a rectangle and the length $L$ , if the width is fixed. Find the area if the length is $11 \mathrm {~cm}$ .
Area (in $\mathrm { cm } ^ { 2 }$ )

A) $156 \mathrm {~cm} ^ { 2 }$
B) $96 \mathrm {~cm} ^ { 2 }$
C) $132 \mathrm {~cm} ^ { 2 }$
D) $108 \mathrm {~cm} ^ { 2 }$

Question 54

Solve.
The height h in feet of a projectile thrown upward from the roof of a building after time t seconds is shown in the graph below. How high will the projectile be after 1.1 seconds?
Height (in ft)
$$\text { Time (in sec) }$$

A)400 ft
B)475 ft
C)450 ft
D)425 ft

Question 55

Solve.
The surface area a of a cylinder is shown in the graph below. What is the radius if the surface area is $30 \mathrm {~m} 2$ ?
Surface Area (in $m ^ { 2 }$ )

A) $1.2 \mathrm {~m}$
B) $0.8 \mathrm {~m}$
C) $1.0 \mathrm {~m}$
D) $1.4 \mathrm {~m}$

Question 56

For the function represented in the graph, determine the domain or range, as requested.
Find the range.

A) $\{ - 5 , - 3 , - 1,1,3 \}$
B) $\{ x \mid 2 \leq x \leq 5 \}$
C) $\{ x \mid - 5 \leq x \leq 3 \}$
D) $\{ 2,3,4,5 \}$

Question 57

For the function represented in the graph, determine the domain or range, as requested.
Find the domain.

A) $\{ - 5 , - 4 , - 3 , - 2 , - 1,0,1,2,3,4,5 \}$
B) $\{ x \mid 0 \leq x \leq 4 \}$
C) $\{ x \mid - 2 \leq x \leq 2 \}$
D) $\{ x \mid 2 \leq x \leq 4 \}$

Question 58

For the function represented in the graph, determine the domain or range, as requested.
Find the range.

A) $\{ - 5 , - 4 , - 3 , - 2 , - 1,0,1,2,3,4,5 \}$
B) $\{ x \mid 2 \leq x \leq - 2 \}$
C) $\{ x \mid - 2 \leq x \leq 2 \}$
D) $\{ x \mid - 4 \leq x \leq 2 \}$

Question 59

The graph of a function f is provided. Determine the requested function value.
$f ( 4 )$

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

Question 60

For the function represented in the graph, determine the domain or range, as requested.
Find the domain.

A) $\{ - 4 , - 3 , - 2 , - 1,0,1,2,3 \}$
B) $\{ - 5 , - 4 , - 3 , - 2 , - 1,0,1,2,3 \}$
C) $\{ x \mid - 4 \leq x \leq 4 \}$
D) $\{ x \mid - 3 \leq x \leq 3 \}$

Question 61

A function f is depicted in the graph. Find any input values that produce the indicated output.
$f(x)=-1$

A) $- 4$
B) $4 , - 2$
C) $- 6,4$
D) $- 4,2$

Question 62

A function f is depicted in the graph. Find any input values that produce the indicated output.
$$f ( x ) = 3$$

A) $\{ x \mid 3 < x \leq 4 \}$
B) 4
C) $\{ x \mid 3 < x < 4 \}$
D) $\{ x \mid 3 \leq x \leq 4 \}$

Question 63

Find the domain.
$$f ( x ) = x ^ { 2 } - 5$$

A) $\{ x \mid x$ is a real number and $x \neq \}$
B) $\{ x \mid x$ is a real number and $x \neq \sqrt { - 5 } \}$
C) $\{ x \mid x$ is a real number and $x z - 5 \}$
D) All real numbers

Question 64

Find the function value.
$f ( - 2 )$

A) 5
B) 6
C) 7
D) 3

Question 65

Find the domain.
$$f ( x ) = - 2 x + 2$$

A) $\{ x \mid x$ is a real number and $x \neq 1 \}$
B) $\{ x \mid x$ is a real number and $x \neq \}$
C) $\{ x \mid x$ is a real number and $x \neq - 2 \}$
D) All real numbers

Question 66

Find the domain.
$$f ( x ) = \frac { - 2 } { 4 - x }$$

A) $\{ x \mid x$ is a real number and $x z - 4 \}$
B) $\{ x \mid x$ is a real number and $x \neq \}$
C) $\{ x \mid x$ is a real number and $x \neq \}$
D) $\{ x \mid x$ is a real number and $x \neq - 2 \}$

Question 67

Find the domain.
$$f ( x ) = x ^ { 3 } - 3$$

A) $\{ x \mid x$ is a real number and $x \neq 3 \}$
B) $\{ x \mid x$ is a real number and $x z - 3 \}$
C) All real numbers
D) $\{ x \mid x$ is a real number and $x \neq \sqrt [ 3 ] { - 3 } \}$

Question 68

Determine the slope and the y-intercept.
$$y = - 0.125 x + 0.4$$

A) Slope $- 0.125 , \mathrm { y }$ -intercept $( 0 , - 0.4 )$
B) Slope $0.4 , \mathrm { y }$ -intercept $( 0 , - 0.125 )$
C) Slope $- 0.125 , \mathrm { y }$ -intercept $( 0,0.4 )$
D) Slope $0.125 , \mathrm { y }$ -intercept $( 0,0.4 )$

Question 69

Determine the slope and the y-intercept.
$$y = 3 x + 4$$

A) Slope 3, y-intercept $( 0,4 )$
B) Slope $4 , \mathrm { y }$ -intercept $( 0 , - 3 )$
C) Slope 4 , y-intercept $( 0,3 )$
D) Slope $- 3 , y$ -intercept $( 0,4 )$

Question 70

Find the domain.
$$f ( x ) = \frac { 1 } { | 5 - x | }$$

A) $\{ x \mid x$ is a real number and $x \neq 5 \}$
B) $\{ x \mid x$ is a real number and $x \neq - 5 \}$
C) All real numbers
D) $\{ x \mid x$ is a real number and $x < 5 \}$

Question 71

Find the domain.
$$f ( x ) = 5 x - 6$$

A) $\{ x \mid x$ is a real number and $x \neq - 8 \}$
B) $\{ x \mid x$ is a real number and $x \neq$
C) $\{ x \mid x$ is a real number and $x \neq \}$
D) All real numbers

Question 72

Find the domain.
$$f ( x ) = \frac { - 9 } { x + 3 }$$

A) $\{ x \mid x$ is a real number and $x \neq 9 \}$
B) $\{ x \mid x$ is a real number and $x z - 3 \}$
C) $\{ x \mid x$ is a real number and $x \neq 3 \}$
D) $\{ x \mid x$ is a real number and $x \neq - 9 \}$

Question 73

Determine the slope and the y-intercept.
$$y = - 6.4 x - 3$$

A) Slope $- 3 , \mathrm { y }$ -intercept $( 0 , - 6.4 )$
B) Slope 6.4, y-intercept $( 0 , - 3 )$
C) Slope $- 3$ , y-intercept $( 0,6.4 )$
D) Slope $- 6.4 , \mathrm { y }$ -intercept $( 0 , - 3 )$

Question 74

The graph of a function f is provided. Determine the requested function value.
$\mathrm { f } ( 1 )$

A) 5

B) 4
C) 1
D) $- 1$

Question 75

Find the function value.
$f(-1)$

A) $- 3$
B) $- 4$
C) $- 5$
D) $- 7$

Question 76

A function f is depicted in the graph. Find any input values that produce the indicated output.
$f(x)=-3$

A) 5
B) 4
C) $- 3$
D) 6

Question 77

A function f is depicted in the graph. Find any input values that produce the indicated output.
$f(x)=-2$

A) 0
B) 2,0
C) $- 1,3$
D) 2

Question 78

Find the domain.
$$f ( x ) = | - 1 x + 4 |$$

A) $\{ x \mid x$ is a real number and $x \neq \}$
B) $\{ x \mid x$ is a real number and $x \neq \}$
C) All real numbers
D) $\{ x \mid x$ is a real number and $x z - 4 \}$

Question 79

A function f is depicted in the graph. Find any input values that produce the indicated output.
$f(x)=2$

A) 0
B) 1
C) 3
D) $- 1$

Question 80

Determine the slope and the y-intercept.
$$f ( x ) = - 4 x - 6$$

A) Slope $4 , \mathrm { y }$ -intercept $( 0 , - 6 )$
B) Slope -6, y-intercept $( 0,4 )$
C) Slope $- 4 , \mathrm { y }$ -intercept $( 0 , - 6 )$
D) Slope $- 6 , \mathrm { y }$ -intercept $( 0 , - 4 )$