College Algebra Essentials

Robert Blitzer

Chapter 2

Functions and Graphs - all with Video Answers

Educators

Section 1

Basics of Functions and Their Graphs

Problem 1

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(1,2),(3,4),(5,5)\}
$$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 2

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(4,5),(6,7),(8,8)\}
$$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 3

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(3,4),(3,5),(4,4),(4,5)\}
$$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 4

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(5,6),(5,7),(6,6),(6,7)\}
$$

Ali Soave

Numerade Educator

Problem 5

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(3,-2),(5,-2),(7,1),(4,9)\}
$$

Ali Soave

Numerade Educator

Problem 6

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(10,4),(-2,4),(-1,1),(5,6)\}
$$

Ali Soave

Numerade Educator

Problem 7

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(-3,-3),(-2,-2),(-1,-1),(0,0)\}
$$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 8

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(-7,-7),(-5,-5),(-3,-3),(0,0)\}
$$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 9

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(1,4),(1,5),(1,6)\}
$$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 10

Determine whether each relation is a function. Give the domain and range for each relation.
$$
\{(4,1),(5,1),(6,1)\}
$$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 11

Determine whether each equation defines $y$ as a function of $x .$
$$
x+y=16
$$

Ali Soave

Numerade Educator

Problem 12

Determine whether each equation defines $y$ as a function of $x .$
$$
x+y=25
$$

Ali Soave

Numerade Educator

Problem 13

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

Lauren Shelton

Numerade Educator

Problem 14

Determine whether each equation defines $y$ as a function of $x .$
$$
x^{2}+y=25
$$

Ali Soave

Numerade Educator

Problem 15

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

Ali Soave

Numerade Educator

Problem 16

Determine whether each equation defines $y$ as a function of $x .$
$$
x^{2}+y^{2}=25
$$

Ali Soave

Numerade Educator

Problem 17

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

Ali Soave

Numerade Educator

Problem 18

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

Ali Soave

Numerade Educator

Problem 19

Determine whether each equation defines $y$ as a function of $x .$
$$
y=\sqrt{x+4}
$$

Ali Soave

Numerade Educator

Problem 20

Determine whether each equation defines $y$ as a function of $x .$
$$
y=-\sqrt{x+4}
$$

Ali Soave

Numerade Educator

Problem 21

Determine whether each equation defines $y$ as a function of $x .$
$$
x+y^{3}=8
$$

Ali Soave

Numerade Educator

Problem 22

Determine whether each equation defines $y$ as a function of $x .$
$$
x+y^{3}=27
$$

Ali Soave

Numerade Educator

Problem 23

Determine whether each equation defines $y$ as a function of $x .$
$$
x y+2 y=1
$$

Ali Soave

Numerade Educator

Problem 24

Determine whether each equation defines $y$ as a function of $x .$
$$
x y-5 y=1
$$

Ali Soave

Numerade Educator

Problem 25

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

Ali Soave

Numerade Educator

Problem 26

Determine whether each equation defines $y$ as a function of $x .$
$$
|x|-y=5
$$

Ali Soave

Numerade Educator

Problem 27

Evaluate each function at the given values of the independent variable and simplify.
$$f(x)=4 x+5$$
a. $f(6)$
b. $f(x+1)$
c. $f(-x)$

Ali Soave

Numerade Educator

Problem 28

Evaluate each function at the given values of the independent variable and simplify.
$$
f(x)=3 x+7
$$
a. $f(4)$
b. $f(x+1) $
c. $f(-x)$

Ali Soave

Numerade Educator

Problem 29

Evaluate each function at the given values of the independent variable and simplify.
$$
g(x)=x^{2}+2 x+3
$$
a. $g(-1)$
b. $g(x+5)$
c. $g(-x)$

Ali Soave

Numerade Educator

Problem 30

Evaluate each function at the given values of the independent variable and simplify.
$$
g(x)=x^{2}-10 x-3
$$
a. $g(-1)$
b. $g(x+2)$
c. $g(-x)$

Ali Soave

Numerade Educator

Problem 31

Evaluate each function at the given values of the independent variable and simplify.
$$
h(x)=x^{4}-x^{2}+1
$$
a. $h(2)$
b. $h(-1)$
c. $h(-x)$
d. $h(3 a)$

Ali Soave

Numerade Educator

Problem 32

Evaluate each function at the given values of the independent variable and simplify.
$$
h(x)=x^{3}-x+1
$$
a. $h(3)$
b. $h(-2)$
c. $h(-x)$
d. $h(3 a)$

Ali Soave

Numerade Educator

Problem 33

Evaluate each function at the given values of the independent variable and simplify.
$$
f(r)=\sqrt{r+6}+3
$$
a. $f(-6)$
b. $f(10)$
c. $f(x-6)$

Ali Soave

Numerade Educator

Problem 34

Evaluate each function at the given values of the independent variable and simplify.
$$
f(r)=\sqrt{25-r}-6
$$
a. $f(16)$
b. $f(-24) $
c. $f(25-2 x)$

Ali Soave

Numerade Educator

Problem 35

Evaluate each function at the given values of the independent variable and simplify.
$$
f(x)=\frac{4 x^{2}-1}{x^{2}}
$$
a. $f(2)$
b. $f(-2)$
c. $f(-x)$

Ali Soave

Numerade Educator

Problem 36

Evaluate each function at the given values of the independent variable and simplify.
$$
f(x)=\frac{4 x^{3}+1}{x^{3}}
$$
a. $f(2)$
b. $f(-2)$
c. $f(-x)$

Ali Soave

Numerade Educator

Problem 37

Evaluate each function at the given values of the independent variable and simplify.
$$
f(x)=\frac{x}{|x|}
$$
a. $f(6)$
b. $f(-6)$
c. $f\left(r^{2}\right)$

Ali Soave

Numerade Educator

Problem 38

Evaluate each function at the given values of the independent variable and simplify.
$$
f(x)=\frac{|x+3|}{x+3}
$$
a. $f(5)$
b. $f(-5)$
c. $f(-9-x)$

Ali Soave

Numerade Educator

Problem 39

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=x, g(x)=x+3
$$

James Kiss

Numerade Educator

Problem 40

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=x, g(x)=x-4
$$

AG

Ankit Gupta

Numerade Educator

Problem 41

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=-2 x, g(x)=-2 x-1
$$

AG

Ankit Gupta

Numerade Educator

Problem 42

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=-2 x, g(x)=-2 x+3
$$

AG

Ankit Gupta

Numerade Educator

Problem 43

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=x^{2}, g(x)=x^{2}+1
$$

AG

Ankit Gupta

Numerade Educator

Problem 44

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=x^{2}, g(x)=x^{2}-2
$$

AG

Ankit Gupta

Numerade Educator

Problem 45

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=|x|, g(x)=|x|-2
$$

AG

Ankit Gupta

Numerade Educator

Problem 46

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=|x|, g(x)=|x|+1
$$

AG

Ankit Gupta

Numerade Educator

Problem 47

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=x^{3}, g(x)=x^{3}+2
$$

AG

Ankit Gupta

Numerade Educator

Problem 48

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=x^{3}, g(x)=x^{3}-1
$$

AG

Ankit Gupta

Numerade Educator

Problem 49

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=3, g(x)=5
$$

Erika Bustos

Numerade Educator

Problem 50

Graph the given functions, $f$ and $g,$ in the same rectangular coordinate system. Select integers for $x$, starting with $-2$ and ending with $2 .$ Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
f(x)=-1, g(x)=4
$$

Ali Soave

Numerade Educator

Problem 51

Graph the given square root functions, $f$ and $g,$ in the same rectangular coordinate system. Use the integer values of $x$ given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of $x$ that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
\begin{aligned}
&f(x)=\sqrt{x} \quad(x=0,1,4,9) \text { and }\\
&g(x)=\sqrt{x}-1 \quad(x=0,1,4,9)
\end{aligned}
$$

Ali Soave

Numerade Educator

Problem 52

Graph the given square root functions, $f$ and $g,$ in the same rectangular coordinate system. Use the integer values of $x$ given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of $x$ that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
\begin{aligned}
&f(x)=\sqrt{x} \quad(x=0,1,4,9) \text { and }\\
&g(x)=\sqrt{x}+2 \quad(x=0,1,4,9)
\end{aligned}
$$

Ali Soave

Numerade Educator

Problem 53

Graph the given square root functions, $f$ and $g,$ in the same rectangular coordinate system. Use the integer values of $x$ given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of $x$ that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
\begin{array}{l}
f(x)=\sqrt{x}(x=0,1,4,9) \text { and } \\
g(x)=\sqrt{x-1} \quad(x=1,2,5,10)
\end{array}
$$

Ali Soave

Numerade Educator

Problem 54

Graph the given square root functions, $f$ and $g,$ in the same rectangular coordinate system. Use the integer values of $x$ given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of $x$ that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of $f$.
$$
\begin{aligned}
&f(x)=\sqrt{x} \quad(x=0,1,4,9) \text { and }\\
&g(x)=\sqrt{x+2} \quad(x=-2,-1,2,7)
\end{aligned}
$$

Ali Soave

Numerade Educator

Problem 55

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 56

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 57

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 58

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 59

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 60

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 61

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 62

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 63

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 64

Use the vertical line test to identify graphs in which $y$ is a function of $x .$
(Graph can't copy)

James Kiss

Numerade Educator

Problem 65

Use the graph of $f$ to find each indicated function value.
(Graph can't copy)
$$
f(-2)
$$

Ali Soave

Numerade Educator

Problem 66

Use the graph of $f$ to find each indicated function value.
(Graph can't copy)
$$
f(2)
$$

Ali Soave

Numerade Educator

Problem 67

Use the graph of $f$ to find each indicated function value.
(Graph can't copy)
$$
f(4)
$$

James Kiss

Numerade Educator

Problem 68

Use the graph of $f$ to find each indicated function value.
(Graph can't copy)
$$
f(-4)
$$

James Kiss

Numerade Educator

Problem 69

Use the graph of $f$ to find each indicated function value.
(Graph can't copy)
$$
f(-3)
$$

James Kiss

Numerade Educator

Problem 70

Use the graph of $f$ to find each indicated function value.
(Graph can't copy)
$$
f(-1)
$$

James Kiss

Numerade Educator

Problem 71

Use the graph of g to solve.
(Graph can't copy)
Find $g(-4)$

James Kiss

Numerade Educator

Problem 72

Use the graph of g to solve.
(Graph can't copy)
Find $g(2)$

James Kiss

Numerade Educator

Problem 73

Use the graph of g to solve.
(Graph can't copy)
Find $g(-10)$

James Kiss

Numerade Educator

Problem 74

Use the graph of g to solve.
(Graph can't copy)
Find $g(10)$

James Kiss

Numerade Educator

Problem 75

Use the graph of g to solve.
(Graph can't copy)
For what value of $x$ is $g(x)=1 ?$

James Kiss

Numerade Educator

Problem 76

Use the graph of g to solve.
(Graph can't copy)
For what value of $x$ is $g(x)=-1 ?$

James Kiss

Numerade Educator

Problem 77

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-2)=? f(2)=?
$$

Yujie Wang

College of San Mateo

Problem 78

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-2)=? \quad f(2)=?
$$

Yujie Wang

College of San Mateo

Problem 79

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-1)=? f(3)=?
$$

Yujie Wang

College of San Mateo

Problem 80

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-4)=? \quad f(3)=?
$$

Yujie Wang

College of San Mateo

Problem 81

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(3)=?
$$

Yujie Wang

College of San Mateo

Problem 82

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-4)=?
$$

Yujie Wang

College of San Mateo

Problem 83

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(4)=?
$$

Yujie Wang

College of San Mateo

Problem 84

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(3)=?
$$

Yujie Wang

College of San Mateo

Problem 85

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-1)=?
$$

Yujie Wang

College of San Mateo

Problem 86

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-2)=?
$$

Yujie Wang

College of San Mateo

Problem 87

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-4)=? f(4)=?
$$

Yujie Wang

College of San Mateo

Problem 88

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-2)=? \quad f(2)=?
$$

Yujie Wang

College of San Mateo

Problem 89

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(4)=?
$$

Yujie Wang

College of San Mateo

Problem 90

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(2)=?
$$

Yujie Wang

College of San Mateo

Problem 91

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-5)+f(3)=?
$$

Yujie Wang

College of San Mateo

Problem 92

Use the graph to determine a. the function's domain; b. the function's range; c. the $x$ -intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
(Graph can't copy)
$$
f(-5)+f(4)=?
$$

Yujie Wang

College of San Mateo

Problem 93

let $f(x)=x^{2}-x+4$ and $g(x)=3 x-5$
Find $g(1)$ and $f(g(1))$

Ali Soave

Numerade Educator

Problem 94

let $f(x)=x^{2}-x+4$ and $g(x)=3 x-5$
Find $g(-1)$ and $f(g(-1))$

Ali Soave

Numerade Educator

Problem 95

let $f$ and $g$ be defined by the following table:
$$
\begin{array}{ccc}
\hline x & f(x) & g(x) \\
\hline-2 & 6 & 0 \\
-1 & 3 & 4 \\
0 & -1 & 1 \\
1 & -4 & -3 \\
2 & 0 & -6
\end{array}
$$
Find $\sqrt{f(-1)-f(0)}-[g(2)]^{2}+f(-2) \div g(2) \cdot g(-1)$

AG

Ankit Gupta

Numerade Educator

Problem 96

let $f$ and $g$ be defined by the following table:
$$
\begin{array}{ccc}
\hline x & f(x) & g(x) \\
\hline-2 & 6 & 0 \\
-1 & 3 & 4 \\
0 & -1 & 1 \\
1 & -4 & -3 \\
2 & 0 & -6
\end{array}
$$
Find $|f(1)-f(0)|-[g(1)]^{2}+g(1) \div f(-1) \cdot g(2)$

AG

Ankit Gupta

Numerade Educator

Problem 97

Find $f(-x)-f(x)$ for the given function $f$ Then simplify the expression.
$$
f(x)=x^{3}+x-5
$$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 98

Find $f(-x)-f(x)$ for the given function $f$ Then simplify the expression.
$$
f(x)=x^{2}-3 x+7
$$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 99

The bar graph shows minimum legal ages for sex and marriage in five selected countries. Use this information to solve Exercises $99-100 .$ (We did not include data for the United States because the legal age of sexual consent varies according to state law. Furthermore, women are allowed to marry younger than men: 16 for women and 18 for men. )
(Bar graph can't copy)
a. Write a set of five ordered pairs in which countries correspond to the minimum legal age of sexual consent. Each ordered pair should be in the form
(country, minimum legal age of sexual consent).
b. Is the relation in part (a) a function? Explain your answer.
c. Write a set of five ordered pairs in which the minimum legal age of sexual consent corresponds to a country. Each ordered pair should be in the form (minimum legal age of sexual consent, country).
d. Is the relation in part (c) a function?

John Irizar

Numerade Educator

Problem 100

The bar graph shows minimum legal ages for sex and marriage in five selected countries. Use this information to solve Exercises $99-100 .$ (We did not include data for the United States because the legal age of sexual consent varies according to state law. Furthermore, women are allowed to marry younger than men: 16 for women and 18 for men. )
(Bar graph can't copy)
a. Write a set of five ordered pairs in which countries correspond to the minimum legal age of marriage with parental consent. Each ordered pair should be in the form
(country, minimum legal age of marriage with parental consent).
b. Is the relation in part (a) a function? Explain your answer.

John Irizar

Numerade Educator

Problem 101

The bar graph shows your chances of surviving to various ages once you reach 60
The functions
$$
\begin{aligned}
f(x) &=-2.9 x+286 \\
\text { and } g(x) &=0.01 x^{2}-4.9 x+370
\end{aligned}
$$
model the chance, as a percent, that a 60 -year-old will survive to age $x .$ Use this information to solve Exercises $101-102$
a. Find and interpret $f(70)$
b. Find and interpret $g(70)$
c. Which function serves as a better model for the chance of surviving to age $70 ?$

Erika Bustos

Numerade Educator

Problem 102

The bar graph shows your chances of surviving to various ages once you reach 60
The functions
$$
\begin{aligned}
f(x) &=-2.9 x+286 \\
\text { and } g(x) &=0.01 x^{2}-4.9 x+370
\end{aligned}
$$
model the chance, as a percent, that a 60 -year-old will survive to age $x .$ Use this information to solve Exercises $101-102$
a. Find and interpret $f(90)$
b. Find and interpret $g(90)$
c. Which function serves as a better model for the chance of surviving to age $90 ?$

Erika Bustos

Numerade Educator

Problem 103

The wage gap is used to compare the status of women's earnings relative to men's. The wage gap is expressed as a percent and is calculated by dividing the median, or middlemost, annual earnings for women by the median annual earnings for men. The bar graph shows the wage gap for selected years from 1980 through 2010 .
(Bar graph can't copy)
The function $G(x)=-0.01 x^{2}+x+60$ models the wage gap, as a percent, $x$ years after $1980 .$ The graph of function G is shown to the right of the actual data. Use this information to solve Exercises $103-104$
a. Find and interpret $G(30)$. Identify this information as a point on the graph of the function.
b. Does $G(30)$ overestimate or underestimate the actual data shown by the bar graph? By how much?

AG

Ankit Gupta

Numerade Educator

Problem 104

The wage gap is used to compare the status of women's earnings relative to men's. The wage gap is expressed as a percent and is calculated by dividing the median, or middlemost, annual earnings for women by the median annual earnings for men. The bar graph shows the wage gap for selected years from 1980 through 2010 .
(Bar graph can't copy)
The function $G(x)=-0.01 x^{2}+x+60$ models the wage gap, as a percent, $x$ years after $1980 .$ The graph of function G is shown to the right of the actual data. Use this information to solve Exercises $103-104$
a. Find and interpret $G(10)$. Identify this information as a point on the graph of the function.
b. Does $G(10)$ overestimate or underestimate the actual data shown by the bar graph? By how much?

AG

Ankit Gupta

Numerade Educator

Problem 105

In Exercises $105-108,$ you will be developing functions that model given conditions.
A company that manufactures bicycles has a fixed cost of $\$ 100,000 .$ It costs $\$ 100$ to produce each bicycle. The total cost for the company is the sum of its fixed cost and variable costs. Write the total cost, $C,$ as a function of the number of bicycles produced, $x .$ Then find and interpret $C(90)$

Yousef Sheikh

Numerade Educator

Problem 106

In Exercises $105-108,$ you will be developing functions that model given conditions.
A car was purchased for $\$ 22,500$. The value of the car decreased by $\$ 3200$ per year for the first six years. Write a function that describes the value of the car, $V,$ after $x$ years, where $0 \leq x \leq 6 .$ Then find and interpret $V(3)$

Yousef Sheikh

Numerade Educator

Problem 107

In Exercises $105-108,$ you will be developing functions that model given conditions.
You commute to work a distance of 40 miles and return on the same route at the end of the day. Your average rate on the return trip is 30 miles per hour faster than your average rate on the outgoing trip. Write the total time, $T,$ in hours, devoted to your outgoing and return trips as a function of your rate on the outgoing trip, $x .$ Then find and interpret $T(30) .$ Hint:
Time traveled $=\frac{\text { Distance traveled }}{\text { Rate of travel }}$

John Irizar

Numerade Educator

Problem 108

In Exercises $105-108,$ you will be developing functions that model given conditions.
A chemist working on a flu vaccine needs to mix a $10 \%$ sodium-iodine solution with a $60 \%$ sodium-iodine solution to obtain a 50 -milliliter mixture. Write the amount of sodium iodine in the mixture, $S,$ in milliliters, as a function of the number of milliliters of the $10 \%$ solution used, $x .$ Then find and interpret $S(30)$

Erika Bustos

Numerade Educator

Problem 109

What is a relation? Describe what is meant by its domain and its range.

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 110

Explain how to determine whether a relation is a function. What is a function?

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 111

How do you determine if an equation in $x$ and $y$ defines $y$ as a function of $x ?$

Ali Soave

Numerade Educator

Problem 112

Does $f(x)$ mean $f$ times $x$ when referring to a function $f ?$ If not, what does $f(x)$ mean? Provide an example with your explanation.

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 113

What is the graph of a function?

James Kiss

Numerade Educator

Problem 114

Explain how the vertical line test is used to determine whether a graph represents a function.

James Kiss

Numerade Educator

Problem 115

Explain how to identify the domain and range of a function from its graph.

James Kiss

Numerade Educator

Problem 116

For people filing a single return, federal income tax is a function of adjusted gross income because for each value of adjusted gross income there is a specific tax to be paid. By contrast, the price of a house is not a function of the lot size on which the house sits because houses on same-sized lots can sell for many different prices.
a. Describe an everyday situation between variables that is
a function.
b. Describe an everyday situation between variables that is not a function.

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 117

Use a graphing utility to verify any five pairs of graphs that you drew by hand in Exercises $39-54$

Ali Soave

Numerade Educator

Problem 118

Determine whether each statement makes sense or does not make sense, and explain your reasoning.
My body temperature is a function of the time of day.

Ali Soave

Numerade Educator

Problem 119

Determine whether each statement makes sense or does not make sense, and explain your reasoning.
Using $f(x)=3 x+2,$ I found $f(50)$ by applying the distributive property to $(3 x+2) 50$

Ali Soave

Numerade Educator

Problem 120

Determine whether each statement makes sense or does not make sense, and explain your reasoning.
I graphed a function showing how paid vacation days depend on the number of years a person works for a company. The domain was the number of paid vacation days.

James Kiss

Numerade Educator

Problem 121

Determine whether each statement makes sense or does not make sense, and explain your reasoning.
I graphed a function showing how the average number of annual physician visits depends on a person's age. The domain was the average number of annual physician visits.

Ali Soave

Numerade Educator

Problem 122

Use the graph of $f$ to determine whether each statement in Exercises $122-125$ is true or false.
(Graph can't copy)
The domain of $f$ is $[-4,-1) \cup(-1,4]$

Ali Soave

Numerade Educator

Problem 123

Use the graph of $f$ to determine whether each statement in Exercises $122-125$ is true or false.
(Graph can't copy)
The range of $f$ is $[-2,2]$

Ali Soave

Numerade Educator

Problem 124

Use the graph of $f$ to determine whether each statement in Exercises $122-125$ is true or false.
(Graph can't copy)
$$
f(-1)-f(4)=2
$$

Ali Soave

Numerade Educator

Problem 125

Use the graph of $f$ to determine whether each statement in Exercises $122-125$ is true or false.
(Graph can't copy)
$$
f(0)=2.1
$$

Ali Soave

Numerade Educator

Problem 126

If $f(x)=3 x+7,$ find $\frac{f(a+h)-f(a)}{h}$

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 127

Give an example of a relation with the following characteristics: The relation is a function containing two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function.

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 128

If $f(x+y)=f(x)+f(y)$ and $f(1)=3,$ find $f(2), f(3)$ and $f(4) .$ Is $f(x+y)=f(x)+f(y)$ for all functions?

Sheila Akinleye

Sheila Akinleye

Numerade Educator

Problem 129

Exercises $129-131$ will help you prepare for the material covered in the next section.
The function $C(t)=20+0.40(t-60)$ describes the monthly cost, $C(t),$ in dollars, for a cellphone plan for $t$ calling minutes, where $t>60 .$ Find and interpret $C(100)$

Ali Soave

Numerade Educator

Problem 130

Exercises $129-131$ will help you prepare for the material covered in the next section.
Use point plotting to graph $f(x)=x+2$ if $x \leq 1$

John Irizar

Numerade Educator

Problem 131

Simplify: $2(x+h)^{2}+3(x+h)+5-\left(2 x^{2}+3 x+5\right)$

Erika Bustos

Numerade Educator