Elementary and Intermediate Algebra

Marvin L. Bittinger, David J. Ellenbogen,Barbara L. Johnson

Chapter 3

Introduction to Graphing and Functions

Educators


Problem 1

Reinforcement In each of Exercises $1-4$ match the set of coordinates with the graph from (a)-(d) below that would be the best for plotting the points.
$$
(-9,3),(-2,-1),(1,5)
$$
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Problem 2

Reinforcement In each of Exercises $1-4$ match the set of coordinates with the graph from (a)-(d) below that would be the best for plotting the points.
$$
(-2,-1),(1,5),(7,3)
$$
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Problem 3

Reinforcement In each of Exercises $1-4$ match the set of coordinates with the graph from (a)-(d) below that would be the best for plotting the points.
$$
(-2,-9),(2,1),(4,-6)
$$
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Problem 4

Reinforcement In each of Exercises $1-4$ match the set of coordinates with the graph from (a)-(d) below that would be the best for plotting the points.
$$
(-2,-1),(-9,3),(-4,-6)
$$
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Problem 5

Driving under the Influence. A blood-alcohol level of $0.08 \%$ or higher makes driving illegal in the United States. This bar graph shows how many drinks a person of a certain weight would need to consume in I $\overline{h r}$ to achieve a blood-alcohol level of $0.08 \% .$ Note that a 12 -oz beer, a 5 -oz glass of wine, or a cocktail containing $1 \frac{1}{2}$ oz of distilled liquor all count as
one drink.
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Approximately how many drinks would a 100 -lb person have consumed in 1 hr to reach a blood-alcohol level of $0.08 \% ?$

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Problem 6

Driving under the Influence. A blood-alcohol level of $0.08 \%$ or higher makes driving illegal in the United States. This bar graph shows how many drinks a person of a certain weight would need to consume in I $\overline{h r}$ to achieve a blood-alcohol level of $0.08 \% .$ Note that a 12 -oz beer, a 5 -oz glass of wine, or a cocktail containing $1 \frac{1}{2}$ oz of distilled liquor all count as
one drink.
CAN'T COPY THE IMAGE
Approximately how many drinks would a 160 -lb person have consumed in 1 hr to reach a blood-alcohol level of $0.08 \% ?$

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Problem 7

Driving under the Influence. A blood-alcohol level of $0.08 \%$ or higher makes driving illegal in the United States. This bar graph shows how many drinks a person of a certain weight would need to consume in I $\overline{h r}$ to achieve a blood-alcohol level of $0.08 \% .$ Note that a 12 -oz beer, a 5 -oz glass of wine, or a cocktail containing $1 \frac{1}{2}$ oz of distilled liquor all count as
one drink.
CAN'T COPY THE IMAGE
What can you conclude about the weight of someone who has consumed 3 drinks in 1 hr without reaching a blood-alcohol level of $0.08 \% ?$

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Problem 8

Driving under the Influence. A blood-alcohol level of $0.08 \%$ or higher makes driving illegal in the United States. This bar graph shows how many drinks a person of a certain weight would need to consume in I $\overline{h r}$ to achieve a blood-alcohol level of $0.08 \% .$ Note that a 12 -oz beer, a 5 -oz glass of wine, or a cocktail containing $1 \frac{1}{2}$ oz of distilled liquor all count as
one drink.
CAN'T COPY THE IMAGE
What can you conclude about the weight of someone who has consumed 4 drinks in 1 hr without reaching a blood-alcohol level of $0.08 \% ?$

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Problem 9

Use the information in Example 2 to answer Exercises $9-12$.
In 2008 , there were $13,803,201$ full-time equivalent students in U.S. colleges and universities. What was the average federal loan per full-time equivalent student?

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Problem 10

Use the information in Example 2 to answer Exercises $9-12$.
In 2008 , there were $13,803,201$ full-time equivalent students in U.S. colleges and universities. What was the average education tax benefit received per fulltime equivalent student?

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Problem 11

Use the information in Example 2 to answer Exercises $9-12$.
Approximately $70 \%$ of state grants are need-based. How much did students receive in 2008 in need-based state grants?

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Problem 12

Use the information in Example 2 to answer Exercises $9-12$.
Approximately $19 \%$ of Pell grant dollars is given to students in for-profit institutions. How much did students in for-profit institutions receive in Pell grants in $2008 ?$

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Problem 13

Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.
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In $2007,$ Americans generated 254 million tons of waste. How much of the waste was glass?

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Problem 14

Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.
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In 2007 , the average American generated 4.62 lb of waste per day. How much of that was paper?

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Problem 15

Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.
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Americans are recycling about $23.7 \%$ of all glass that is in the waste stream. How much glass did Americans recycle in $2007 ? \text { (See Exercise } 13 .)$

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Problem 16

Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.
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Americans are recycling about $54.5 \%$ of all paper. What amount of paper did the average American recycle per day in $2007 ?$ (Use the information in Exercise $14 .)$

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Problem 17

The graph below shows the number of U.S. households with only wireless phones.
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Approximately how many households were wireless only in $2005 ?$

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Problem 18

The graph below shows the number of U.S. households with only wireless phones.
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Approximately how many households were wireless only in $2008 ?$

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Problem 19

The graph below shows the number of U.S. households with only wireless phones.
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The graph below shows the number of U.S. households with only wireless phones.
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Problem 20

The graph below shows the number of U.S. households with only wireless phones.
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By how much did the number of wireless-only households increase from 2005 to $2006 ?$

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Problem 21

Plot each group of points.
$$
(1,2),(-2,3),(4,-1),(-5,-3),(4,0),(0,-2)
$$

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Problem 22

Plot each group of points.
$$
(-2,-4),(4,-3),(5,4),(-1,0),(-4,4),(0,5)
$$

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Problem 23

Plot each group of points.
$$
\begin{aligned}
&(4,4),(-2,4),(5,-3),(-5,-5),(0,4),(0,-4)\\
&(3,0),(-4,0)
\end{aligned}
$$

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Problem 24

Plot each group of points.
$$
\begin{aligned}
&(2,5),(-1,3),(3,-2),(-2,-4),(0,4),(0,-5)\\
&(5,0),(-5,0)
\end{aligned}
$$

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Problem 25

Listed below are estimates of the number of text messages sent in the United States. Make a line graph of the data.
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Problem 26

Make a line graph of the data in the table below, listing years on the horizontal scale.
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Problem 27

In Exercises $27-30,$ find the coordinates of points $A, B, C$ $D,$ and $E$.
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Problem 28

In Exercises $27-30,$ find the coordinates of points $A, B, C$ $D,$ and $E$.
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Problem 29

In Exercises $27-30,$ find the coordinates of points $A, B, C$ $D,$ and $E$.
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Problem 30

In Exercises $27-30,$ find the coordinates of points $A, B, C$ $D,$ and $E$.
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Problem 31

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
$$
(-75,5),(-18,-2),(9,-4)
$$

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Problem 32

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
$$
(-13,3),(48,-1),(62,-4)
$$

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Problem 33

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
$$
(-1,83),(-5,-14),(5,37)
$$

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Problem 34

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
$$
(2,-79),(4,-25),(-4,12)
$$

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Problem 35

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
$$
(-10,-4),(-16,7),(3,15)
$$

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Problem 36

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
$$
(5,-16),(-7,-4),(12,3)
$$

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Problem 37

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.

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Problem 38

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
$$
(750,-8),(-150,17),(400,32)
$$

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Problem 39

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
$$
(-83,491),(-124,-95),(54,-238)
$$

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Problem 40

In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
$$
(738,-89),(-49,-6),(-165,53)
$$

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Problem 41

In which quadrant or on which axis is each point located?
$$
(7,-2)
$$

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Problem 42

In which quadrant or on which axis is each point located?
$$
(-1,-4)
$$

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Problem 43

In which quadrant or on which axis is each point located?
$$
(-4,-3)
$$

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Problem 44

In which quadrant or on which axis is each point located?
$$
(1,-5)
$$

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Problem 45

In which quadrant or on which axis is each point located?
$$
(0,-3)
$$

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Problem 46

In which quadrant or on which axis is each point located?
$$
(6,0)
$$

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Problem 47

In which quadrant or on which axis is each point located?
$$
(-4.9,8.3)
$$

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Problem 48

In which quadrant or on which axis is each point located?
$$
(7.5,2.9)
$$

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Problem 49

In which quadrant or on which axis is each point located?
$$
\left(-\frac{5}{2}, 0\right)
$$

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Problem 50

In which quadrant or on which axis is each point located?
$$
(0,2.8)
$$

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Problem 51

In which quadrant or on which axis is each point located?
$$
(160,2)
$$

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Problem 52

In which quadrant or on which axis is each point located?
$$
\left(-\frac{1}{2}, 2000\right)
$$

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Problem 53

In which quadrants are the first coordinates positive?

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Problem 54

In which quadrants are the second coordinates negative?

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Problem 55

In which quadrants are the second coordinates negative?

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Problem 56

In which quadrants do the first and second coordinates have opposite signs?

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Problem 57

For Exercises $57-60,$ set up the indicated viewing window on a graphing calculator, choosing appropriate scales for the axes. Choice of scale may vary.
$$
[-3,15,-50,500]
$$

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Problem 58

For Exercises $57-60,$ set up the indicated viewing window on a graphing calculator, choosing appropriate scales for the axes. Choice of scale may vary.
$$
[-8000,0,-100,600]
$$

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Problem 59

For Exercises $57-60,$ set up the indicated viewing window on a graphing calculator, choosing appropriate scales for the axes. Choice of scale may vary.
$$
\left[-\frac{1}{2}, 1,0,0.1\right]
$$

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Problem 60

For Exercises $57-60,$ set up the indicated viewing window on a graphing calculator, choosing appropriate scales for the axes. Choice of scale may vary.
$$
\left[-2.6,2.6,-\frac{1}{4}, \frac{1}{4}\right]
$$

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Problem 61

The graph below was included in a mailing sent by Agway $^{\mathscr{Q}}$ to their oil customers in 2000 . What information is missing from the graph and why is the graph misleading?
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Problem 62

What do all of the points on the vertical axis of a graph have in common?

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Problem 63

To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$
$$
5 y=2 x
$$

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Problem 64

To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$
$$
2 y=-3 x
$$

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Problem 65

To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$
$$
x-y=8
$$

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Problem 66

To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$
$$
2 x+5 y=10
$$

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Problem 67

To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$
$$
2 x+3 y=5
$$

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Problem 68

To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$
$$
5 x-8 y=1
$$

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Problem 69

Describe what the result would be if the first and second coordinates of every point in the following graph of an arrow were interchanged.
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Problem 70

The graph accompanying Example 3 flattens out. Why do you think this occurs?

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Problem 71

In which quadrant(s) could a point be located if its coordinates are opposites of each other?

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Problem 72

In which quadrant(s) could a point be located if its coordinates are reciprocals of each other?

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Problem 73

The points $(-1,1),(4,1),$ and $(4,-5)$ are three vertices of a rectangle. Find the coordinates of the fourth vertex.

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Problem 74

The pairs $(-2,-3),(-1,2),$ and $(4,-3)$ can serve as three (of four) vertices for three different parallelograms. Find the fourth vertex of each parallelogram.

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Problem 75

Graph eight points such that the sum of the coordinates in each pair is $7 .$ Answers may vary.

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Problem 76

Find the perimeter of a rectangle if three of its vertices are $(5,-2),(-3,-2),$ and $(-3,3)$

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Problem 77

Find the area of a triangle whose vertices have coordinates $(0,9),(0,-4),$ and $(5,-4)$

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Problem 78

Coordinates can also be used to describe the location on a sphere: 0" latitude is the equator and 0' longitude is a line from the North Pole to the South Pole through France and Algeria. In the figure shown here, hurricane Clara is at a point about 260 mi northwest of Bermuda near latitude $36.0^{\circ}$ North, longitude 69.0^{\circ} West.
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Approximate the latitude and the longitude of Bermuda.

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Problem 79

Coordinates can also be used to describe the location on a sphere: 0" latitude is the equator and 0' longitude is a line from the North Pole to the South Pole through France and Algeria. In the figure shown here, hurricane Clara is at a point about 260 mi northwest of Bermuda near latitude $36.0^{\circ}$ North, longitude 69.0^{\circ} West.
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Approximate the latitude and the longitude of Lake Okeechobee.

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Problem 80

In the Star Trek science-fiction series, a threedimensional coordinate system is used to locate objects in space. If the center of a planet is used as the origin, how many "quadrants" will exist? Why? If possible, sketch a three-dimensional coordinate system and label each "quadrant"

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