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Elementary and Intermediate Algebra

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

Chapter 3

Introduction to Graphing and Functions - all with Video Answers

Educators


Section 1

Reading Graphs, Plotting Points, and Scaling Graphs

00:22

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.
$$
(-9,3),(-2,-1),(1,5)
$$
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
00:16

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.
$$
(-2,-1),(1,5),(7,3)
$$
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
00:21

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.
$$
(-2,-9),(2,1),(4,-6)
$$
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
00:16

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.
$$
(-2,-1),(-9,3),(-4,-6)
$$
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
00:26

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.
CAN'T COPY THE IMAGE
Approximately how many drinks would a 100 -lb person have consumed in 1 hr to reach a blood-alcohol level of $0.08 \% ?$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:30

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 $0.08 \% ?$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:51

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 $0.08 \% ?$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:32

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 $0.08 \% ?$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:57

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?

Sarah Wharton
Sarah Wharton
Numerade Educator
01:15

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?

Sarah Wharton
Sarah Wharton
Numerade Educator
00:43

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?

Sarah Wharton
Sarah Wharton
Numerade Educator
01:03

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 $2008 ?$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:51

Problem 13

Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.
CAN'T COPY THE CHART
In $2007,$ Americans generated 254 million tons of waste. How much of the waste was glass?

Sarah Wharton
Sarah Wharton
Numerade Educator
00:34

Problem 14

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:52

Problem 15

Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.
CAN'T COPY THE CHART
Americans are recycling about $23.7 \%$ of all glass that is in the waste stream. How much glass did Americans recycle in $2007 ? \text { (See Exercise } 13 .)$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:00

Problem 16

Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.
CAN'T COPY THE CHART
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 $14 .)$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:19

Problem 17

The graph below shows the number of U.S. households with only wireless phones.
CAN'T COPY THE IMAGE
Approximately how many households were wireless only in $2005 ?$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:21

Problem 18

The graph below shows the number of U.S. households with only wireless phones.
CAN'T COPY THE IMAGE
Approximately how many households were wireless only in $2008 ?$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:32

Problem 19

The graph below shows the number of U.S. households with only wireless phones.
CAN'T COPY THE IMAGE

Sarah Wharton
Sarah Wharton
Numerade Educator
00:48

Problem 20

The graph below shows the number of U.S. households with only wireless phones.
CAN'T COPY THE IMAGE
By how much did the number of wireless-only households increase from 2005 to $2006 ?$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:24

Problem 21

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:27

Problem 22

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:39

Problem 23

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:31

Problem 24

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

Sarah Wharton
Sarah Wharton
Numerade Educator
02:42

Problem 25

Listed below are estimates of the number of text messages sent in the United States. Make a line graph of the data.
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
02:09

Problem 26

Make a line graph of the data in the table below, listing years on the horizontal scale.
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
01:00

Problem 27

In Exercises $27-30,$ find the coordinates of points $A, B, C$ $D,$ and $E$.
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
00:50

Problem 28

In Exercises $27-30,$ find the coordinates of points $A, B, C$ $D,$ and $E$.
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
00:52

Problem 29

In Exercises $27-30,$ find the coordinates of points $A, B, C$ $D,$ and $E$.
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
00:52

Problem 30

In Exercises $27-30,$ find the coordinates of points $A, B, C$ $D,$ and $E$.
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
01:36

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.
$$
(-75,5),(-18,-2),(9,-4)
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:36

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.
$$
(-13,3),(48,-1),(62,-4)
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:22

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.
$$
(-1,83),(-5,-14),(5,37)
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:40

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.
$$
(2,-79),(4,-25),(-4,12)
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:55

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.
$$
(-10,-4),(-16,7),(3,15)
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:13

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.
$$
(5,-16),(-7,-4),(12,3)
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:05

Problem 37

In Exercises $31-40,$ use a grid 10 squares wide and 10 squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.
(-100,-5),(350,20),(800,37)

Sarah Wharton
Sarah Wharton
Numerade Educator
01:21

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.
$$
(750,-8),(-150,17),(400,32)
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:25

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.
$$
(-83,491),(-124,-95),(54,-238)
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
01:30

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.
$$
(738,-89),(-49,-6),(-165,53)
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:24

Problem 41

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:22

Problem 42

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:22

Problem 43

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:21

Problem 44

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:25

Problem 45

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:20

Problem 46

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:30

Problem 47

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:23

Problem 48

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:23

Problem 49

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:25

Problem 50

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:20

Problem 51

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:26

Problem 52

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:49

Problem 53

In which quadrants are the first coordinates positive?

Sarah Wharton
Sarah Wharton
Numerade Educator
00:47

Problem 54

In which quadrants are the second coordinates negative?

Sarah Wharton
Sarah Wharton
Numerade Educator
00:46

Problem 55

In which quadrants do both coordinates have the same sign?

Sarah Wharton
Sarah Wharton
Numerade Educator
00:44

Problem 56

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:33

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.
$$
[-3,15,-50,500]
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:35

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.
$$
[-8000,0,-100,600]
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:34

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.
$$
\left[-\frac{1}{2}, 1,0,0.1\right]
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:38

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.
$$
\left[-2.6,2.6,-\frac{1}{4}, \frac{1}{4}\right]
$$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:30

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?
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
00:33

Problem 62

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:39

Problem 63

To prepare for Section 3.2 , review solving for a variable (Section 2.3).
$5 y=2 x$

Sarah Wharton
Sarah Wharton
Numerade Educator
00:31

Problem 64

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:55

Problem 65

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:03

Problem 66

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:59

Problem 67

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:26

Problem 68

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:13

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.
CAN'T COPY THE GRAPH

Sarah Wharton
Sarah Wharton
Numerade Educator
01:10

Problem 70

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:52

Problem 71

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:28

Problem 72

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:48

Problem 73

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:29

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.

Maria Dearborn
Maria Dearborn
Numerade Educator
01:25

Problem 75

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:24

Problem 76

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

Sarah Wharton
Sarah Wharton
Numerade Educator
01:22

Problem 77

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

Sarah Wharton
Sarah Wharton
Numerade Educator
00:24

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.
CAN'T COPY THE IMAGE
Approximate the latitude and the longitude of Bermuda.

Sarah Wharton
Sarah Wharton
Numerade Educator
00:16

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.
CAN'T COPY THE IMAGE
Approximate the latitude and the longitude of Lake Okeechobee.

Sarah Wharton
Sarah Wharton
Numerade Educator
00:46

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"

Sarah Wharton
Sarah Wharton
Numerade Educator