Coburn J.W., Herdlick J.D. College Algebra: Graphs and Models
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xviii
Mid-Chapter Checks
Mid-Chapter Checks provide students with a good stopping
place to assess their knowledge before moving on to the
second half of the chapter.
Solid Skill Development . . .
Throu
g
h Exercise
s
g
We have included a wealth of exercises in support of each section’s main ideas. The exercise
sets were constructed with great care, in an effort to provide support for weaker students,
while challenging more advanced students to reach even further. The quantity and quality of
exercises offers strong support for a teacher’s efforts, and numerous opportunities to guide
students through difficult calculations and to illustrate important problem solving ideas.
—
The Authors
End-of-Section Exercise Sets
▶
Concepts and Vocabulary exercises to help students
recall and retain important terms.
▶
Extending the Concept exercises that require
communication of topics, synthesis of related
concepts, and the use of higher-order thinking
skills.
2. Transformations that change only the location of a
graph and not its shape or form, include
and .
䊳
CONCEPTS AND VOCABULARY
Fill in each blank with the appropriate word or phrase. Carefully reread the section if needed.
2.2 EXERCISES
1. After a vertical , points on the graph are
farther from the x-axis. After a vertical ,
points on the graph are closer to the x-axis.
3. The vertex of is at
and the graph opens .
h1x2 31x 52
2
9 4. The inflection point of is
at and the end-behavior is , .
f 1x221x 42
3
11
5 Gi th h f l f ti f( )di /
6 Di /E l i h th hift f if 12
2
3
15. 16.
17. 18.
5
y
h(x)
5
y
g(x)
h1x22 1x 1 4g1x2 2 14 x
55
5
5
x
y
f(x)
55
5
5
x
y
r(x)
f 1x2 2 1x 1 4r 1x2314 x 3
䊳
DEVELOPING YOUR SKILLS
By carefully inspecting each graph given, (a) identify the
function family; (b) describe or identify the end-behavior,
vertex, intervals where the function is increasing or
decreasing, maximum or minimum value(s) and x- and
y-intercepts; and (c) determine the domain and range.
Assume required features have integer values.
7. 8.
55
5
5
x
y
55
5
5
x
y
g1x2x
2
2xf 1x2 x
2
4x
䊳
WORKING WITH FORMULAS
61. Discriminant of the reduced cubic
The discriminant of a cubic equation is less well known than that of the quadratic, but serves the same purpose.
The discriminant of the reduced cubic is given by the formula shown, where p is the linear coefficient and q is
the constant term. If there will be three real and distinct roots. If there are still three real roots, but
one is a repeated root (multiplicity two). If there are one real and two complex roots. Suppose we wish to
study the family of cubic equations where
a. Verify the resulting discriminant is
b. Determine the values of p and q for which this family of equations has a repeated real root. In other words,
solve the equation using the rational zeroes theorem and synthetic division
to write D in completely factored form.
14p
3
27p
2
54p 272 0
D 14p
3
27p
2
54p 272.
q p 1.
D 6 0,
D 0,D 7 0,
x
3
ⴙ px ⴙ q ⴝ 0: D ⴝⴚ14p
3
ⴙ 27q
2
2
䊳
EXTENDING THE CONCEPT
59. Use the general solutions from the quadratic formula
to show that the average value of the x-intercepts is
. Explain/Discuss why the result is valid even if
the roots are complex.
b 2b
2
4acb 2b
2
4ac
b
2a
62. Referring to Exercise 39, discuss the nature (real or
complex, rational or irrational) and number of
zeroes (0, 1, or 2) given by the vertex/intercept
formula if (a) a and k have like signs, (b) a and k
have unlike signs, (c) k is zero, (d) the ratio
is positive and a perfect square and (e) the
k
a
䊳
MAINTAINING YOUR SKILLS
37. (1.3) Is the graph shown here, the graph of a
function? Discuss why or why not.
38. (R.2/R.3) Determine
the area of the figure
shown
39. (1.5) Solve for r:
40 lf if ibl
A P Prt
1A LW, A r
2
2.
24 cm
18 cm
1. Determine whether the following function is even,
odd, or neither.
2. Use a graphing calculator to find the maximum and
minimum values of
. Round to
the nearest hundredth.
3 Use interval notation to identify the interval(s)
f 1x21.91x
4
2.3x
3
2.2x 5.12
f
1x2 x
2
冟
x
冟
4x
4. Write the equation of the function that has the same
graph of , shifted left 4 units and up 2
units.
5. For the graph given, (a) identify
the function family, (b) describe
or identify the end-behavior,
inflection point, and x- and
y-intercepts, (c) determine
the domain and range and
f 1x2 2x
Exercise 5
55
5
x
y
f(x)
MID-CHAPTER CHECK
▶
Developing Your Skills exercises to provide
practice of relevant concepts just learned with
increasing levels of difficulty.
▶
Working with Formulas exercises to demonstrate
contextual applications of well-known formulas.
▶
Maintaining Your Skills exercises that address
skills from previous sections to help students
retain previously learning knowledge.
3
9
.
(
1
.5
)
S
o
lv
e
f
or
r
:
A
P
Prt
40
Sl
f
(if
ib
l)
“
There seems to be a good selection of easy, moderate,
and difficult problems in the exercises.
”
—Ed Gallo, Sinclair Community College
xviii
retain
previously
learning
knowledge.
“
The exercise sets are plentiful. I like having many to
choose from when assigning homework. When there
are only one or two exercises of a particular type, it’s
hard for the students to get the practice they need.
”
—Sarah Jackson, Pratt Community College
▶
Worki
ng
with Formulas exer
ci
ses to
d
emonstrate
“
The sections in the assignments headed working with
formulas and applications bring forward some interesting
ideas and problems that are more in depth. These would
help hold the students’ interest in the topic.
”
—Sherri Rankin, Huchinson Community College
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xix
MAKING CONNECTIONS
Making Connections: Graphically, Symbolically, Numerically, and Verbally
Eight graphs (a) through (h) are given. Match the characteristics shown in 1 through 16 to one of the eight graphs.
55
5
5
x
y
55
5
5
x
y
55
5
5
x
y
55
5
5
x
y
1. ____
2. ____ y x 1
y
1
3
x 1
(a) (b) (c) (d)
55
5
5
x
y
55
5
5
x
y
55
5
5
x
y
55
5
5
x
y
(e) (f) (g) (h)
9. ____
10. ____ , f
142 3f 142 3
f
112 0f 132 4,
End-of-Chapter Review Material
Exercises located at the end of the chapter provide students
with the tools they need to prepare for a quiz or test. Each
chapter features the following:
SECTION 1.1 Rectangular Coordinates; Graphing Circles and Other Relations
KEY CONCEPTS
•
A relation is a collection of ordered pairs (x, y) and can be stated as a set or in equation form.
•
As a set of ordered pairs, we say the relation is pointwise-defined. The domain of the relation is the set of all first
coordinates, and the range is the set of all corresponding second coordinates.
•
A relation can be expressed in mapping notation , indicating an element from the domain is mapped to
(corresponds to or is associated with) an element from the range.
•
The graph of a relation in equation form is the set of all ordered pairs (x, y) that satisfy the equation. We plot a
sufficient number of points and connect them with a straight line or smooth curve, depending on the pattern
formed.
•
The x- and y-variables of linear equations and their graphs have implied exponents of 1.
•
With a relation entered on the screen, a graphing calculator can provide a table of ordered pairs and the
related graph.
•
The midpoint of a line segment with endpoints (x
1
, y
1
) and (x
2
, y
2
) is .
•
The distance between the points (x
1
, y
1
) and (x
2
, y
2
) is .
•
The equation of a circle centered at (h, k) with radius r is .
EXERCISES
1. Represent the relation in mapping notation, then state the domain and range.
2
517, 32, 14, 22, 15, 12, 17, 02, 13, 22, 10, 826
1x h2
2
1y k2
2
r
2
d 21x
2
x
1
2
2
1y
2
y
1
2
2
a
x
1
x
2
2
,
y
1
y
2
2
b
Y=
x S y
SUMMARY AND CONCEPT REVIEW
▶
Making Connections matching exercises are groups of
problems where students must identify graphs based on
an equation or description. This feature helps students
make the connection between graphical and algebraic
information while it enhances students’ ability to read
and interpret graphical data.
▶
Chapter Summary and Concept Reviews that present
key concepts with corresponding exercises by section in
a format easily used by students.
▶
Practice Tests that give students the opportunity to check
their knowledge and prepare for classroom quizzes, tests,
and other assessments.
▶
Cumulative Reviews that are presented at the end of
each chapter help students retain previously learned
skills and concepts by revisiting important ideas from
earlier chapters (starting with Chapter 2).
▶
Graphing Calculator icons appear next to exercises
where important concepts can be supported by the
use of graphing technology.
SE
K
E
•
yy
“
The problem sets are really magnificent. I deeply enjoy
and appreciate the many problems that incorporate
telescopes, astronomy, reflector design, nuclear cooling
tower profiles, charged particle trajectories, and
other such examples from science, technology, and
engineering.
”
—Light Bryant, Arizona Western College
MAK
ING
CO
NNE
CTI
ONS
Mki C ti G hi ll S bli ll N i ll dV bll
“
Not only was the algebra rigorously treated, but it
was reinforced throughout the chapters with the Mid-
Chapter Check and the Chapter Review and Tests.
”
—Mark Crawford, Waubonsee Community College
Homework Selection Guide
A list of suggested homework exercises has been provided for each section of the text (Annotated Instructor’s Edition only).
This feature may prove especially useful for departments that encourage consistency among many sections, or those having a
large adjunct population. The feature was also designed as a convenience to instructors, enabling them to develop an inventory
of exercises that is more in tune with the course as they like to teach it. The guide provides prescreened and preselected
assignments at four different levels: Core, Standard, Extended, and In Depth.
• Core: These assignments go right to the heart of the material,
offering a minimal selection of exercises that cover the primary
concepts and solution strategies of the section, along with a
small selection of the best applications.
• Standard: The assignments at this level include the Core exercises, while providing for additional practice without excessive drill.
A wider assortment of the possible variations on a theme are included, as well as a greater variety of applications.
• Extended: Assignments from the Extended category expand on the Standard exercises to include more applications, as well
as some conceptual or theory-based questions. Exercises may include selected items from the Concepts and Vocabulary,
Working with Formulas, and the Extending the Concept categories of the exercise sets.
• In Depth: The In Depth assignments represent a more comprehensive look at the material from each section, while
attempting to keep the assignment manageable for students. These include a selection of the most popular and highest-quality
exercises from each category of the exercise set, with an additional emphasis on Maintaining Your Skills.
p
8
13
3
10
19
2
HOMEWORK SELECTION GUIDE
Core: 7–91 every other odd, 95–101 odd (26 Exercises)
Standard: 1–4, 7–83 every other odd, 85–92 all, 95–101 odd (36 Exercises)
Extended: 1–4, 7–31 every other odd, 35–38 all, 39–79 every other odd,
85–92 all, 95–101 odd,106,109 (39 Exercises)
In Depth: 1–4, 7–31 every other odd, 35–38 all, 39–83 every other odd,
85–92 all, 95, 96, 98, 99,100,101, 105,106,109 (44 Exercises)
Additional answers can be found in the Instructor Answer Appendix.
“
The authors give very good uses of the calculator in every
section. I have been using TI calculators for 15 years and
I learned a few new tricks while reading this book.
”
—George Hurlburt, Corning Community College
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While examples and applications are arguably the most prominent features of a mathematics text,
it’s the readability and writing style of the authors that bind them together. It may be true that
some students don’t read the text, and that others open the text only when looking for an example
similar to the exercise they’re working on. But when they do and for those students that do (read
the text), it’s important they have a text that “speaks to them,” relating concepts in a form and
at a level they understand and can relate to. We feel the writing style of this text will help draw
students in and keep their interest, becoming a positive experience and bringing them back a second
and third time, until it becomes habitual. At this point students might begin to see the true value
of their text, as it becomes a resource for learning on equal footing with any other form of
supplemental instruction. This text represents our best efforts in this direction. —The Authors
Strong Mathmatical Connections . . .
xx
Through a Conversational Writing Style
Conversational Writing Style
John and J.D.’s experience in the classroom and their strong connections
to how students comprehend the material are evident in their writing
style. They use a conversational and supportive writing style, providing
the students with a tool they can depend on when the teacher is not
available, when they miss a day of class, or simply when working on
their own. The effort they have put into the writing is representative of
John Coburn’s unofficial mantra: “If you want more students to reach
the top, you gotta put a few more rungs on the ladder.”
Through Student Involvement
How do you design a student-friendly textbook? We decided to get students involved by hosting
two separate focus groups. During these sessions we asked students to advise us on how they use their books, what
pedagogical elements are useful, which elements are distracting and not useful,
as well as general feedback on page layout. During this process there were
times when we thought, “Now why hasn’t anyone ever thought of that before?”
Clearly these student focus groups were invaluable. Taking direct student
feedback and incorporating what is feasible and doesn’t detract from instructor
use of the text is the best way to design a truly student-friendly text. The next
two pages will highlight what we learned from students so you can see for
yourself how their feedback played an important role in the development of the
Coburn/Herdlick series.
“
Coburn strikes a good balance between
providing all of the important information
necessary for a certain topic without going
too deep.
”
—Barry Monk, Macon State College
“
I think the authors have done an excellent job
of interweaving the formal explanations with the
‘plain talk’ descriptions, illustrating with
meaningful examples and applications.
”
—Ken Gamber, Hutchinson Community College
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EXAMPLE 4
䊳
Graphing Exponential Functions Using Transformations
Graph using transformations of
the basic function (not by simply plotting
points). Clearly state what transformations are
applied.
Solution
䊳
The graph of F is that of the basic function
with a horizontal shift 1 unit right and
a vertical shift 2 units up. With this in mind the
horizontal asymptote also shifts from to
and (0, 1) shifts to (1, 3). The y-intercept of
F is at (0, 2.5):
To help sketch a more accurate graph, the point (3, 6) can be used:
Now try Exercises 15 through 30
䊳
F132 6.
2.5
1
2
2
2
1
2
F102 2
1021
2
y 2
y 0
f
1x2 2
x
f 1x2 2
x
F1x2 2
x1
2
x
44
y
(1, 3)
(3, 6)
(0, 2.5)
F(x) = 2
x
is shifted
1 unit right
2 units up
y 2
B. You’ve just seen how
we can graph general
exponential functions
Demographics is the statistical study of human populations. In this section, we intro-
duce the family of exponential functions, which are widely used to model population
growth or decline with additional applications in science, engineering, and many other
fields. As with other functions, we begin with a study of the graph and its characteristics.
A. Evaluating Exponential Functions
In the boomtowns of the old west, it was not
uncommon for a town to double in size every year
(at least for a time) as the lure of gold drew more
and more people westward. When this type of
growth is modeled using mathematics, exponents
play a lead role. Suppose the town of Goldsboro
h d 1000 id t h ld fi t di d
LEARNING OBJECTIVES
In Section 5.2 you will see
how we can:
A. Evaluate an exponential
function
B. Graph general
exponential functions
C. Graph base-e
exponential functions
D. Solve exponential
equations and
applications
5.2 Exponential Functions
xxi
CAUTION
䊳
For equations like those in Example 1, be careful not to treat the absolute value bars as
simple grouping symbols. The equation has only the solution
and “misses” the second solution since it yields in simplified form.
The equation simplifies to and there are actually two
solutions. Also note that !5
冟
x 7
冟
冟
5x 35
冟
冟
x 7
冟
35
冟
x 7
冟
2 13
x 7 3x 10,
51x 72 2 13
Students asked for Check Points
throughout each section to alert them
when a specific learning objective has
been covered and to reinforce the use
of correct mathematical terms.
Students said that Learning Objectives
should clearly define the goals of each
section.
Students told us that the color red should
only be used for things that are really
important. Also, anything significant
should be included in the body of the
text; marginal readings imply optional.
Sd ld h h l dh ld
Described by students as one of the
most useful features in a math text,
Caution Boxes signal a student to stop
and take note in order to avoid mistakes
in problem solving.
Students told us they liked when the
examples were linked to the exercises.
Examples are called out in the margins
so they are easy for students to spot.
Students said having a lot of icons was
confusing. The graphing calculator is the
only icon used in the exercise sets; no
unnecessary icons are used.
䊳
APPLICATIONS
Use the information given to build a linear equation
model, then use the equation to respond. For exercises
71 to 74, develop both an algebraic and a graphical
solution.
71. Business depreciation: A business purchases a
copier for $8500 and anticipates it will depreciate
in value $1250 per year.
a. What is the copier’s value after 4 yr of use?
b. How many years will it take for this copier’s
value to decrease to $2250?
72. Baseball card value: After purchasing an
autographed baseball card for $85, its value
increases by $1.50 per year.
a. What is the card’s value 7 yr after purchase?
b. How many years will it take for this card’s
value to reach $100?
74. Gas mileage: When empty, a large dump-truck
gets about 15 mi per gallon. It is estimated that for
each 3 tons of cargo it hauls, gas mileage decreases
by mi per gallon.
a. If 10 tons of cargo is being carried, what is the
truck’s mileage?
b. If the truck’s mileage is down to 10 mi per
gallon, how much weight is it carrying?
75. Parallel/nonparallel roads: Aberville is 38 mi
north and 12 mi west of Boschertown, with a
straight “farm and machinery” road (FM 1960)
connecting the two cities. In the next county,
Crownsburg is 30 mi north and 9.5 mi west of
Dower, and these cities are likewise connected by a
straight road (FM 830). If the two roads continued
indefinitely in both directions, would they intersect
at some point?
3
4
x
ponential Functions Using Trans
f
ormatio
ns
ifi
f
x
1
Examples are “boxed” so students can
clearly see where they begin and end.
Students told us that directions should be
in bold so they are easily distinguishable
from the problems.
Because students spend a lot of time in
the exercise section of a text, they said
that a white background is hard on their
eyes . . . so we used a soft, off-white color
for the background.
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College Algebra
Second Edition
Review ◆ Equations and Inequalities ◆ Relations,
Functions, and Graphs ◆ Polynomial and Rational
Functions ◆ Exponential and Logarithmic Functions
◆ Systems of Equations and Inequalities ◆ Matrices
◆ Geometry and Conic Sections ◆ Additional
Topics in Algebra
MHID 0-07-351941-3, ISBN 978-0-07-351941-8
College Algebra Essentials
Second Edition
Review ◆ Equations and Inequalities ◆ Relations,
Functions, and Graphs ◆ Polynomial and Rational
Functions ◆ Exponential and Logarithmic Functions
◆ Systems of Equations and Inequalities
MHID 0-07-351968-5, ISBN 978-0-07-351968-5
Algebra and Trigonometry
Second Edition
Review ◆ Equations and Inequalities ◆ Relations,
Functions, and Graphs ◆ Polynomial and Rational
Functions ◆ Exponential and Logarithmic Functions
◆ Trigonometric Functions ◆ Trigonometric
Identities, Inverses, and Equations ◆ Applications
of Trigonometry ◆ Systems of Equations and Inequalities ◆ Matrices
◆ Geometry and Conic Sections ◆ Additional Topics in Algebra
MHID 0-07-351952-9, ISBN 978-0-07-351952-4
Coburn’s Precalculus Series
Precalculus
Second Edition
Equations and Inequalities ◆ Relations,
Functions, and Graphs ◆ Polynomial and
Rational Functions ◆ Exponential and
Logarithmic Functions ◆ Trigonometric
Functions ◆ Trigonometric Identities,
Inverses, and Equations ◆ Applications of Trigonometry
◆ Systems of Equations and Inequalities ◆ Matrices ◆ Geometry
and Conic Sections ◆ Additional Topics in Algebra ◆ Limits
MHID 0-07-351942-1, ISBN 978-0-07-351942-5
Trigonometry
Second Edition
Introduction to Trigonometry ◆ Right
Triangles and Static Trigonometry
◆ Radian Measure and Dynamic
Trigonometry ◆ Trigonometric Graphs
and Models ◆ Trigonometric Identities
◆ Inverse Functions and Trigonometric Equations
◆ Applications of Trigonometry ◆ Trigonometric
Connections to Algebra
MHID 0-07-351948-0, ISBN 978-0-07-351948-7
Precalculus: Graphs & Models, First Edition
Functions and Graphs ◆ Relations; More on Functions ◆ Quadratic Functions and
Operations on Functions ◆ Polynomial and Rational Functions ◆ Exponential and
Logarithmic Functions ◆ Introduction to Trigonometry ◆ trigonometric Identities,
Inverses, and Equations ◆ Applications of Trigonometry ◆ Systems of Equations and
Inequalities; Matrices ◆ Analytic Geometry; Polar and parametric Equations ◆ Sequences,
Series, Counting, and Probability ◆ Bridges to Calculus—An Introduction to Limits
College Algebra: Graphs & Models, First Edition
A Review of Basic Concepts and Skills ◆ Functions and Graphs ◆ Relations; More on
Functions ◆ Quadratic Functions and Operations on Functions ◆ Polynomial and
Rational Functions ◆ Exponential and Logarithmic Functions ◆ Systems of Equations
and Inequalities ◆ Matrices and Matrix Applications ◆ Analytic Geometry and the
Conic Sections ◆ Additional Topics in Algebra
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A key principle in the development of any mathemat-
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Francisco Arceo, Illinois State University
Candace Banos, Southeastern Louisiana University
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Nicholas Curtis, Southeastern Louisiana University
M. D. “Boots” Feltenberger, Southeastern Louisiana
University
Regina Foreman, Southeastern Louisiana University
Ashley Lae, Southeastern Louisiana University
Brian Lau, Illinois State University
Daniel Nathan Mielneczek, Illinois State University
Mingaile Orakauskaite, Illinois State University
Todd Michael Rapnikas, Illinois State University
Bethany Rollet, Illinois State University
Teddy Schrishuhn, Illinois State University
Special Thanks
Sherry Meier, Illinois State University
Rebecca Muller, Southeastern Louisiana University
Anne Schmidt, Illinois State University
Digital Contributors
Josh Schultz, Illinois State University
Jessica Smith, Southeastern Louisiana University
Andy Thurman, Illinois State University
Ashley Youngblood, Southeastern Louisiana University
Jeremy Coffelt, Blinn College
Vanessa Coffelt, Blinn College
Vickie Flanders, Baton Rouge Community College
Anne Marie Mosher, Saint Louis Community College-
Florissant Valley
Kristen Stoley, Blinn College
David Ray, University of Tennessee-Martin
Stephen Toner, Victor Valley Community College
Paul Vroman, Saint Louis Community College-Florissant
Valley
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Developmental Editing
The manuscript has been impacted by numerous developmental reviewers who edited for clarity and consistency. Efforts
resulted in cutting length from the manuscript, while retaining a conversational and casual narrative style. Editorial
work also ensured the positive visual impact of art and photo placement.
Chapter Reviews and Manuscript Reviews
Teachers and academics from across the country reviewed
the current edition text, the proposed table of contents, and
first-draft manuscript to give feedback on reworked narrative,
design changes, pedagogical enhancements, and organizational
changes. This feedback was summarized by the book team and
used to guide the direction of the second-draft manuscript.
Betty Anderson, Howard Community College
David Bosworth, Hutchinson Community College
Daniel Brock, Arkansas State University-Beebe
Barry Brunson, Western Kentucky University
Light Bryant, Arizona Western College
Brenda Burns-Williams, North Carolina State
University-Raleigh
Charles Cooper, Hutchinson Community College
Mark Crawford, Waubonsee Community College
Joseph Demaio, Kennesaw State University
Alvio Dominguez, Miami-Dade College-Wolfson
Dale Duke, Oklahoma City Community College
Frank Edwards, Southeastern Louisiana University
Caleb Emmons, Pacific University
Mike Everett, Santa Ana College
Maggie Flint, Northeast State Technical Community College
Ed Gallo, Sinclair Community College
Ken Gamber, Hutchinson Community College
David Gurney, Southeastern Louisiana University
Sally Haas, Angelina College
Ben Hill, Lane Community College
Jody Hinson, Cape Fear Community College
Lynda Hollingsworth, Northwest Missouri State University
George Hurlburt, Corning Community College
Sarah Jackson, Pratt Community College
Laud Kwaku, Owens Community College
Kathryn Lavelle, Westchester Community College
Joseph Lloyd Harris, Gulf Coast Community College
Austin Lovenstein, Pulaski Technical College
Rodolfo Maglio, Northeastern Illinois University
Barry Monk, Macon State College
Camille Moreno, Cosumnes River College
Anne Marie Mosher, Saint Louis Community
College-Florissant Valley
Lilia Orlova, Nassau Community College
Susan Pfeifer, Butler Community College
Sherri Rankin, Hutchinson Community College
Daniel Russow, Arizona Western College-Yuma
Rose Shirey, College of the Mainland
Joy Shurley, Abraham Baldwin Agricultural College
Sean Simpson, Westchester Community College
Pam Stogsdill, Bossier Parish Community College
Allison Sutton, Austin Community College
Linda Tremer, Three Rivers Community Collge
Dahlia Vu, Santa Ana College
Jackie Wing, Angelina College
Acknowledgments
We first want to express a deep appreciation for the guidance,
comments, and suggestions offered by all reviewers of the
manuscript. We have once again found their collegial exchange
of ideas and experience very refreshing and instructive, and
always helping to create a better learning tool for our students.
Vicki Krug has continued to display an uncanny ability
to bring innumerable pieces from all directions into a unified
whole, in addition to providing spiritual support during some
extremely trying times; Patricia Steele’s skill as a copy editor
is as sharp as ever, and her attention to detail continues to
pay great dividends; which helps pay the debt we owe Katie
White, Michelle Flomenhoft, Christina Lane, and Eve Lipton
for their useful suggestions, infinite patience, tireless efforts,
and art-counting eyes, which helped in bringing the manu-
script to completion. We must also thank John Osgood for his
ready wit, creative energies, and ability to step into the flow
without missing a beat; Laurie Janssen and our magnificent
design team, and Dawn Bercier whose influence on this project
remains strong although she has moved on, as it was her inde-
fatigable spirit that kept the ship on course through trial and
tempest, and her ski-jumper’s vision that brought J.D. on board.
In truth, our hats are off to all the fine people at McGraw-Hill
for their continuing support and belief in this series. A final
word of thanks must go to Rick Armstrong, whose depth of
knowledge, experience, and mathematical connections seems
endless; Anne Marie Mosher for her contributions to various
features of the text, Mitch Levy for his consultation on the exer-
cise sets, Stephen Toner for his work on the videos, Jon Booze
and his team for their work on the test bank, Cindy Trimble for
her invaluable ability to catch what everyone else misses; and
to Rick Pescarino, Kelly Ballard, John Elliot, Jim Frost, Barb
Kurt, Lillian Seese, Nate Wilson, and all of our colleagues at St.
Louis Community College, whose friendship, encouragement,
and love of mathematics makes going to work each day a joy.
Making Connections . . .
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Through Supplements
*All online supplements are available through the book’s website: www.mhhe.com/coburn.
Instructor Supplements
• Computerized Test Bank Online: Utilizing
Brownstone Diploma
®
algorithm-based testing software
enables users to create customized exams quickly.
• Instructor’s Solutions Manual: Provides comprehensive,
worked-out solutions to all exercises in the text.
• Annotated Instructor’s Edition: Contains all answers to
exercises in the text, which are printed in a second color,
adjacent to corresponding exercises, for ease of use by the
instructor.
Student Supplements
• Student Solutions Manual provides comprehensive,
worked-out solutions to all of the odd-numbered
exercises.
• Graphing Calculator Manual includes detailed
instructions for using different calculator models to solve
problems throughout the text. Written by the authors
to accompany their text, it is designed to match and
supplement the text.
• Videos
• Interactive video lectures are provided for each section
in the text, which explain to the students how to do key
problem types, as well as highlighting common
mistakes to avoid.
• Exercise videos provide step-by-step instruction for the
key exercises which students will most wish to see
worked out.
• Graphing calculator videos help students master the
most essential calculator skills used in the college
algebra course.
• The videos are closed-captioned for the hearing
impaired, subtitled in Spanish, and meet the Americans
with Disabilities Act Standards for Accessible Design.
Connect Math™ Hosted by ALEKS®
www.connectmath.com
Connect Math Hosted by ALEKS is an exciting, new assess-
ment and assignment platform combining the strengths of
McGraw-Hill Higher Education and ALEKS Corporation.
Connect Math Hosted by ALEKS is the first platform on the
market to combine an artificial-intelligent, diagnostic
assessment with an intuitive ehomework platform designed
to meet your needs.
Connect Hosted by ALEKS is the culmination of a
one-of-a-kind market development process involving math
full-time faculty members and adjuncts at every step of the
process. This process enables us to provide you with an end
product that better meets your needs.
Connect Math Hosted by ALEKS is built by mathemati-
cians educators for mathematicians educators!
www.aleks.com
ALEKS (Assessment and LEarning in Knowledge Spaces) is
a dynamic online learning system for mathematics education,
available over the Web 24/7. ALEKS assesses students, accu-
rately determines their knowledge, and then guides them to
the material that they are most ready to learn. With a variety
of reports, Textbook Integration Plus, quizzes, and homework
assignment capabilities, ALEKS offers flexibility and ease of
use for instructors.
• ALEKS uses artificial intelligence to determine exactly
what each student knows and is ready to learn. ALEKS
remediates student gaps and provides highly efficient
learning and improved learning outcomes
• ALEKS is a comprehensive curriculum that aligns with
syllabi or specified textbooks. Used in conjunction with
McGraw-Hill texts, students also receive links to text-
specific videos, multimedia tutorials, and textbook pages.
• ALEKS offers a dynamic classroom management system
that enables instructors to monitor and direct student
progress toward mastery of course objectives.
ALEKS Prep/Remediation:
• Helps instructors meet the challenge of remediating
underprepared or improperly placed students.
• Assesses students on their prerequisite knowledge needed
for the course they are entering (i.e., Calculus students are
tested on Precalculus knowledge) and prescribes a unique
and efficient learning path specifically to address their
strengths and weaknesses.
• Students can address prerequisite knowledge gaps outside
of class freeing the instructor to use class time pursuing
course outcomes.
Making Connections . . .
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McGraw-Hill Higher Education and Blackboard
®
have teamed up.
Blackboard, the Web-based course-management system, has partnered with McGraw-Hill
to better allow students and faculty to use online materials and activities to complement
face-to-face teaching. Blackboard features exciting social learning and teaching tools
that foster more logical, visually impactful and active learning opportunities for students.
You’ll transform your closed-door classrooms into communities where students remain
connected to their educational experience 24 hours a day.
This partnership allows you and your students access to McGraw-Hill’s Connect™
and Create™ right from within your Blackboard course—all with one single sign-on.
Not only do you get single sign-on with Connect and Create, you also get deep inte-
gration of McGraw-Hill content and content engines right in Blackboard. Whether you’re
choosing a book for your course or building Connect assignments, all the tools you need
are right where you want them—inside of Blackboard.
Gradebooks are now seamless. When a student completes an integrated Connect
assignment, the grade for that assignment automatically (and instantly) feeds your Black-
board grade center.
McGraw-Hill and Blackboard can now offer you easy access to industry leading
technology and content, whether your campus hosts it, or we do. Be sure to ask your local
McGraw-Hill representative for details.
TEGRITY—tegritycampus.mhhe.com
McGraw-Hill Tegrity Campus™ is a service that makes class time available all the time by
automatically capturing every lecture in a searchable format for students to review when
they study and complete assignments. With a simple one-click start and stop process, you
capture all computer screens and corresponding audio. Students replay any part of any
class with easy-to-use browser-based viewing on a PC or Mac.
Educators know that the more students can see, hear, and experience class resources,
the better they learn. With Tegrity, students quickly recall key moments by using Tegrity’s
unique search feature. This search helps students efficiently find what they need, when
they need it across an entire semester of class recordings. Help turn all your students’ study
time into learning moments immediately supported by your lecture.
To learn more about Tegrity watch a 2-minute Flash demo at tegritycampus.mhhe.com.
Electronic Books:
If you or your students are ready for an alternative version of the traditional textbook,
McGraw-Hill eBooks offer a cheaper and eco-friendly alternative to traditional textbooks.
By purchasing eBooks from McGraw-Hill, students can save as much as 50% on selected
titles delivered on the most advanced eBook platform available. Contact your McGraw-Hill
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Create:
Craft your teaching resources to match the way you teach! With McGraw-Hill Create,
www.mcgrawhillcreate.com, you can easily rearrange chapters, combine material from
other content sources, and quickly upload content you have written like your course syl-
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Go to www.mcgrawhillcreate.com today and register to experience how McGraw-Hill
Create empowers you to teach your students your way.
Making Connections . . .
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Preface vi
Index of Applications xxxii
CHAPTER R A Review of Basic Concepts and Skills 1
R.1 Algebraic Expressions and the Properties of Real Numbers 2
R.2 Exponents, Scientific Notation, and a Review of Polynomials 11
R.3 Solving Linear Equations and Inequalities 25
R.4 Factoring Polynomials and Solving Polynomial Equations
by Factoring 39
R.5 Rational Expressions and Equations 53
R.6 Radicals, Rational Exponents, and Radical Equations 65
Overview of Chapter R: Prerequisite Definitions, Properties, Formulas, and
Relationships 81
CHAPTER 1 Relations, Functions, and Graphs 85
1.1 Rectangular Coordinates; Graphing Circles and Other Relations 86
1.2 Linear Equations and Rates of Change 103
1.3 Functions, Function Notation, and the Graph of a Function 117
Mid-Chapter Check 132
Reinforcing Basic Concepts: Finding the Domain and Range of a Relation
from Its Graph 132
1.4 Linear Functions, Special Forms, and More on Rates of Change 134
1.5 Solving Equations and Inequalities Graphically; Formulas
and Problem Solving 148
1.6 Linear Function Models and Real Data 163
Making Connections 177
Summary and Concept Review 178
Practice Test 183
Strengthening Core Skills: The Various Forms of a Linear Equation 184
Calculator Exploration and Discovery: Evaluating Expressions and Looking
for Patterns 185
CHAPTER 2 More on Functions 187
2.1 Analyzing the Graph of a Function 188
2.2 The Toolbox Functions and Transformations 202
2.3 Absolute Value Functions, Equations, and Inequalities 218
Mid-Chapter Check 228
Reinforcing Basic Concepts: Using Distance to Understand Absolute Value
Equations and Inequalities
229
2.4 Basic Rational Functions and Power Functions;
More on the Domain 230
2.5 Piecewise-Defined Functions 245
Contents
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