Coburn J.W. Algebra and Trigonometry
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CHAPTER 8 Systems of Equations and Inequalities
• The coverage of systems and matrices has been split into two chapters for the second edition (Chapter 8 on systems
and Chapter 9 on matrices).
• Section 8.1 includes improved coverage of equivalent systems in addition to more examples and exercises having to
do with distance and navigation.
• Section 8.2 features improved coverage of dependent and inconsistent systems.
• Section 8.3 now presents nonlinear systems before linear programming and features a better presentation of
nonlinear and nonpolynomial systems.
• More business examples and exercises have also been added to Section 8.3.
• New applications of linear programming are found in Section 8.4.
CHAPTER 9 Matrices and Matrix Applications
• Section 9.1 features an added example of Gauss-Jordan Elimination.
• Section 9.2 includes better sequencing of examples and improved coverage of matrix properties.
• Coverage of determinants has been streamlined with more development given to determinants in Section 9.3,
while improved coverage of partial fractions and a better introduction of the decomposition template is found in
Section 9.4.
CHAPTER 10 Analytical Geometry and the Conic Sections
• New Section 10.1 presents a brief introduction to analytical geometry to provide a better bridge to the conic sections
and show why cone/conic connection is important.
• Greater emphasis on the connection between ellipses and circles is featured in section 10.2.
• Exercises requiring the movement from graph to equation have been added throughout the chapter.
CHAPTER 11 Additional Topics in Algebra
• The exposition has been revised throughout Chapter 11 for increased clarity and improved flow of topics.
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Accuracy Panel
A selected trio of key instructors served as the chief advisors for the accuracy and clarity of the text and
solutions manual. These individuals reviewed the final manuscript, the page proofs in first and revised
rounds, as well as the writing and accuracy check of the instructor’s solutions manuals. This trio, in
addition to several other accuracy professionals, gives you the assurance of accuracy.
J.D. Herdlick, St. Louis Community College–Meramac
Richard A. Pescarino, St. Louis Community College–Florissant Valley
Nathan G. Wilson, St. Louis Community College–Meramac
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xxii
Student Focus Groups
Two student focus groups were held at Illinois State
University and Southeastern Louisiana University to engage
students in the development process and provide feedback as
to how the design of a textbook impacts homework and study
habits in the College Algebra and Precalculus course areas.
Francisco Arceo, Illinois State University
Dave Cepko, Illinois State University
Andrea Connell, Illinois State 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
Josh Schultz, Illinois State University
Andy Thurman, Illinois State University
Candace Banos, Southeastern Louisiana University
Nicholas Curtis, Southeastern Louisiana University
M. D. “Boots” Feltenberger, Southeastern Louisiana
University
Regina Foreman, Southeastern Louisiana University
Ashley Lae, Southeastern Louisiana University
Jessica Smith, Southeastern Louisiana University
Ashley Youngblood, Southeastern Louisiana University
Special Thanks
Sherry Meier, Illinois State University
Rebecca Muller, Southeastern Louisiana University
Anne Schmidt, Illinois State University
Instructor Focus Groups
Focus groups held at Baton Rouge Community College and ORMATYC provided feedback on the new Connections
to Calculus feature in Precalculus, and shed light on the coverage of review material in this course. User focus
groups at Southeastern Louisiana University and Madison Area Technical College confirmed the organizational
changes planned for the second edition, provided feedback on the interior design, and helped us enhance and refine
the strengths of the first edition.
Virginia Adelmann, Southeastern Louisiana University
George Alexander, Madison Area Technical College
Kenneth R. Anderson, Chemeketa Community College
Wayne G.Barber, Chemeketa Community College
Thomas Dick, Oregon State University
Vickie Flanders, Baton Rouge Community College
Bill Forrest, Baton Rouge Community College
Susan B. Guidroz, Southeastern Louisiana University
Christopher Guillory, Baton Rouge Community College
Cynthia Harrison, Baton Rouge Community College
Judy Jones, Madison Area Technical College
Lucyna Kabza, Southeastern Louisiana University
Ann Kirkpatrick, Southeastern Louisiana University
Sunmi Ku, Bellevue Community College
Pamela Larson, Madison Area Technical College
Jennifer Laveglia, Bellevue Community College
DeShea Miller, Southeastern Louisiana University
Elizabeth Miller, Southeastern Louisiana University
Rebecca Muller, Southeastern Louisiana University
Donna W. Newman, Baton Rouge Community College
Scott L. Peterson, Oregon State University
Ronald Posey, Baton Rouge Community College
Ronni Settoon, Southeastern Louisiana University
Jeganathan Sriskandarajah, Madison Area Technical
College
Martha Stevens, Bellevue Community College
Mark J. Stigge, Baton Rouge Community College
Nataliya Svyeshnikova, Southeastern Louisiana University
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xxiii
John N. C. Szeto, Southeastern Louisiana University
Christina C. Terranova, Southeastern Louisiana University
Amy S. VanWey, Clackamas Community College
Andria Villines, Bellevue Community College
Jeff Weaver, Baton Rouge Community College
Ana Wills, Southeastern Louisiana University
Randall G. Wills, Southeastern Louisiana University
Xuezheng Wu, Madison Area Technical College
Developmental Symposia
McGraw-Hill conducted two symposia directly related to the development of Coburn’s second edition. These events
were an opportunity for editors from McGraw-Hill to gather information about the needs and challenges of instructors
teaching these courses and confirm the direction of the second edition.
Diary Reviews and Class Tests
Users of the first edition, Said Ngobi and Stephen Toner of Victor Valley College, provided chapter-by chapter
feedback in diary form based on their experience using the text. Board of Advisors members facilitated class tests
of the manuscript for a given topic. Both instructors and students returned questionnaires detailing their thoughts
on the effectiveness of the text’s features.
Class Tests
Instructors
Bill Forrest, Baton Rouge Community College
Marc Grether, University of North Texas
Sharon Hamsa, Metropolitan Community College–Longview
Rita Marie O’Brien’s , Navarro College
Students
Cynthia Aguilar, Navarro College
Michalann Amoroso, Baton Rouge Community College
Chelsea Asbill, Navarro College
Sandra Atkins, University of North Texas
Robert Basom, University of North Texas
Cynthia Beasley, Navarro College
Michael Bermingham, University of North Texas
Jennifer Bickham, Metropolitan Community College–Longview
Rachel Brokmeier, Baton Rouge Community College
Amy Brugg, University of North Texas
Zach Burke, University of North Texas
Shaina Canlas, University of North Texas
Kristin Chambers, University of North Texas
Brad Chatelain, Baton Rouge Community College
Yu Yi Chen, Baton Rouge Community College
Jasmyn Clark, Baton Rouge Community College
Belinda Copsey, Navarro College
Melissa Cowan, Metropolitan Community College–Longview
Katlin Crooks, Baton Rouge Community College
Rachele Dudley, University of North Texas
Kevin Ekstrom, University of North Texas
Jade Fernberg, University of North Texas
Joseph Louis Fino, Jr., Baton Rouge Community College
Shannon M. Fleming, University of North Texas
Travis Flowers, University of North Texas
Teresa Foxx, University of North Texas
Michael Giulietti, University of North Texas
Michael Gordon, Navarro College
Rohan Dalpatadu, University of Nevada–Las Vegas
Franco Fedele, University of West Florida
Bill Forrest, Baton Rouge Community College
Marc Grether, University of North Texas
Sharon Hamsa, Metropolitan Community College–Longview
Derek Hein, Southern Utah University
Rebecca Heiskell, Mountain View College
Terry Hobbs, Metropolitan Community College–
Maple Woods
Klay Kruczek, Western Oregon University
Nancy Matthews, University of Oklahoma
Sherry Meier, Illinois State University
Mary Ann (Molly) Misko, Gadsden State Community College
Rita Marie O’Brien, Navarro College
Jason Pallett, Metropolitan Community College–
Longview
Christopher Parks, Indiana University–Bloomington
Vicki Partin, Bluegrass Community College
Philip Pina, Florida Atlantic University–Boca
Nancy Ressler, Oakton Community College,
Des Plaines Campus
Vicki Schell, Pensacola Junior College
Kenan Shahla, Antelope Valley College
Linda Tansil, Southeast Missouri State University
Stephen Toner, Victor Valley College
Christine Walker, Utah Valley State College
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xxiv
Hayley Hentzen, University of North Texas
Courtney Hodge, University of North Texas
Janice Hollaway, Navarro College
Weslon Hull, Baton Rouge Community College
Sarah James, Baton Rouge Community College
Georlin Johnson, Baton Rouge Community College
Michael Jones, Navarro College
Robert Koon, Metropolitan Community College–Longview
Ben Lenfant, Baton Rouge Community College
Colin Luke, Baton Rouge Community College
Lester Maloney, Baton Rouge Community College
Ana Mariscal, Navarro College
Tracy Ann Nguyen, Baton Rouge Community College
Alexandra Ortiz, University of North Texas
Robert T. R. Paine, Baton Rouge Community College
Kade Parent, Baton Rouge Community College
Brittany Louise Pratt, Baton Rouge Community College
Brittney Pruitt, Metropolitan Community College–Longview
Paul Rachal, Baton Rouge Community College
Matt Rawls, Baton Rouge Community College
Adam Reichert, Metropolitan Community College–Longview
Ryan Rodney, Baton Rouge Community College
Cody Scallan, Baton Rouge Community College
Laura Shafer, University of North Texas
Natina Simpson, Navarro College
Stephanie Sims, Metropolitan Community College–Longview
Cassie Snow, University of North Texas
Justin Stewart, Metropolitan Community College–Longview
Marjorie Tulana, Navarro College
Ashleigh Variest, Baton Rouge Community College
James A. Wann, Navarro College
Amber Wendleton, Metropolitan Community College–Longview
Eric Williams, Metropolitan Community College–Longview
Katy Wood, Metropolitan Community College–Longview
Developmental Editing
The manuscript has been impacted by numerous developmental editors 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.
First Edition Chapter Reviews
and Manuscript Reviews
Over 200 instructors participated in postpublication single
chapter reviews of the first edition and helped the team
build the revision plan for the second edition. Over 100
teachers and academics from across the country reviewed
the current edition text, the proposed second edition table
of contents, and first-draft second edition 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.
Scott Adamson, Chandler-Gilbert Community College
Teresa Adsit, University of Wisconsin–Green Bay
Ebrahim Ahmadizadeh, Northampton Community College
George M. Alexander, Madison Area Technical College
Frances Alvarado, University of Texas–Pan American
Deb Anderson, Antelope Valley College
Philip Anderson, South Plains College
Michael Anderson, West Virginia State University
Jeff Anderson, Winona State University
Raul Aparicio, Blinn College
Judith Barclay, Cuesta College
Laurie Battle, Georgia College and State University
Annette Benbow, Tarrant County College–Northwest
Amy Benvie, Florida Gulf Coast University
Scott Berthiaume, Edison State College
Wes Black, Illinois Valley Community College
Arlene Blasius, SUNY College of Old Westbury
Caroline Maher Boulis, Lee University
Amin Boumenir, University of West Georgia
Terence Brenner, Hostos Community College
Gail Brooks, McLennan Community College
G. Robert Carlson, Victor Valley College
Hope Carr, East Mississippi Community College
Denise Chellsen, Cuesta College
Kim Christensen, Metropolitan Community College–
Maple Woods
Lisa Christman, University of Central Arkansas
John Church, Metropolitan Community College–Longview
Sarah Clifton, Southeastern Louisiana University
David Collins, Southwestern Illinois College
Sarah V. Cook, Washburn University
Rhonda Creech, Southeast Kentucky Community and
Technical College
Raymond L. Crownover, Gateway College of Evangelism
Marc Cullison, Connors State College
Steven Cunningham, San Antonio College
Callie Daniels, St. Charles Community College
John Denney, Northeast Texas Community College
Donna Densmore, Bossier Parish Community College
Alok Dhital, University of New Mexico–Gallup
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xxv
James Michael Dubrowsky Wayne Community College
Brad Dyer, Hazzard Community & Technical College
Sally Edwards, Johnson County Community College
John Elliott, St. Louis Community College–Meramec
Gay Ellis, Missouri State University
Barbara Elzey, Bluegrass Community College
Dennis Evans, Concordia University Wisconsin
Samantha Fay, University of Central Arkansas
Victoria Fischer, California State University–Monterey Bay
Dorothy French, Community College of Philadelphia
Eric Garcia, South Texas College
Laurice Garrett, Edison College
Ramona Gartman, Gadsden State Community College–
Ayers Campus
Scott Gaulke, University of Wisconsin–Eau Claire
Scott Gordon, University of West Georgia
Teri Graville, Southern Illinois University Edwardsville
Marc Grether, University of North Texas
Shane Griffith, Lee University
Gary Grohs, Elgin Community College
Peter Haberman, Portland Community College
Joseph Harris, Gulf Coast Community College
Margret Hathaway, Kansas City Community College
Tom Hayes, Montana State University
Bill Heider, Hibbling Community College
Max Hibbs, Blinn College
Terry Hobbs, Metropolitan Community College–Maple Woods
Sharon Holmes, Tarrant County College–Southeast
Jamie Holtin, Freed-Hardeman University
Brian Hons, San Antonio College
Kevin Hopkins, Southwest Baptist University
Teresa Houston, East Mississippi Community College
Keith Hubbard, Stephen F. Austin State University
Jeffrey Hughes, Hinds Community College–Raymond
Matthew Isom, Arizona State University
Dwayne Jennings, Union University
Judy Jones, Madison Area Technical College
Lucyna Kabza, Southeastern Louisiana University
Aida Kadic-Galeb, University of Tampa
Cheryl Kane, University of Nebraska
Rahim Karimpour, Southern Illinois University Edwardsville
Ryan Kasha, Valencia Community College
David Kay, Moorpark College
Jong Kim, Long Beach City College
Lynette King, Gadsden State Community College
Carolyn Kistner, St. Petersburg College
Barbara Kniepkamp, Southern Illinois University Edwardsville
Susan Knights, Boise State University
Stephanie Kolitsch, University of Tennessee at Martin
Louis Kolitsch, University of Tennessee at Martin
William Kirby, Gadsden State Community College
Karl Kruczek, Northeastern State University
Conrad Krueger, San Antonio College
Marcia Lambert, Pitt Community College
Rebecca Lanier, Bluegrass Community College
Marie Larsen, Cuesta College
Pam Larson, Madison Area Technical College
Jennifer Lawhon, Valencia Community College
John Levko, University of Scranton
Mitchel Levy, Broward Community College
John Lofberg, South Dakota School of Mines and Technology
Mitzi Logan, Pitt Community College
Sandra Maldonado, Florida Gulf Coast University
Robin C. Manker, Illinois College
Manoug Manougian, University of South Florida
Nancy Matthews, University of Oklahoma
Roger McCoach, County College of Morris
James McKinney, California Polytechnic State University–
Pomona
Jennifer McNeilly, University of Illinois Urbana Champaign
Kathleen Miranda, SUNY College at Old Westbury
Mary Ann (Molly) Misko, Gadsden State Community College
Marianne Morea, SUNY College of Old Westbury
Michael Nasab, Long Beach City College
Said Ngobi, Victor Valley College
Tonie Niblett, Northeast Alabama Community College
Gary Nonnemacher, Bowling Green State University
Elaine Nye, Alfred State College
Rhoda Oden, Gadsden State Community College
Jeannette O’Rourke, Middlesex County College
Darla Ottman, Elizabethtown Community & Technical
College
Jason Pallett, Metropolitan Community College–Longview
Priti Patel, Tarrant County College–Southeast
Judy Pennington-Price, Midway College
Susan Pfeifer, Butler County Community College
Margaret Poitevint, North Georgia College & State University
Tammy Potter, Gadsden State Community College
Debra Prescott, Central Texas College
Elise Price, Tarrant County College
Kevin Ratliff, Blue Ridge Community College
Bruce Reid, Howard Community College
Jolene Rhodes, Valencia Community College
Karen Rollins, University of West Georgia
Randy Ross, Morehead State University
Michael Sawyer, Houston Community College
Richard Schnackenberg, Florida Gulf Coast University
Bethany Seto, Horry-Georgetown Technical College
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xxvi
Delphy Shaulis, University of Colorado–Boulder
Jennifer Simonton, Southwestern Illinois College
David Slay, McNeese State University
David Snyder, Texas State University at San Marcos
Larry L. Southard, Florida Gulf Coast University
Lee Ann Spahr, Durham Technical Community College
Jeganathan Sriskandarajah, Madison Area Technical College
Adam Stinchcombe, Eastern Arizona College
Pam Stogsdill, Bossier Parish Community College
Eleanor Storey, Front Range Community College
Kathy Stover, College of Southern Idaho
Mary Teel, University of North Texas
Carlie Thompson, Southeast Kentucky Community
& Technical College
Bob Tilidetzke, Charleston Southern University
Stephen Toner, Victor Valley College
Thomas Tunnell, Illinois Valley Community College
Carol Ulsafer, University of Montana
John Van Eps, California Polytechnic State University–San
Luis Obispo
Andrea Vorwark, Metropolitan Community College–Maple
Woods
Jim Voss, Front Range Community College
Jennifer Walsh, Daytona State College
Jiantian Wang, Kean University
Sheryl Webb, Tennessee Technological University
Bill Weber, Fort Hays State University
John Weglarz, Kirkwood Community College
Tressa White, Arkansas State University–Newport
Cheryl Winter, Metropolitan Community College–Blue River
Kenneth Word, Central Texas College
Laurie Yourk, Dickinson State University
Acknowledgments
I first want to express a deep appreciation for the guidance,
comments and suggestions offered by all reviewers of the
manuscript. I 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.
I would especially like to thank Vicki Krug for her
uncanny ability to bring innumerable pieces from all direc-
tions into a unified whole; Patricia Steele for her eagle-eyed
attention to detail; Katie White and Michelle Flomenhoft for
their helpful suggestions, infinite patience, tireless efforts,
and steady hand in bringing the manuscript to completion;
John Osgood for his ready wit and creative energies, Laurie
Janssen and our magnificent design team, and Dawn Bercier,
the master of this large ship, whose indefatigable spirit kept
the ship on course through trial and tempest, and brought us
all safely to port. In truth, my hat is 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; J. D. Herdlick for his friendship
and his ability to fill an instant and sudden need, Anne Marie
Mosher for her contributions to various features of the text,
Mitch Levy for his consultation on the exercise sets, Stephen
Toner for his work on the videos, Rosemary Karr for her
meticulous work on the solutions manuals, Jay Miller and
Carrie Green for their invaluable ability to catch what every-
one else misses; and to Rick Pescarino, Nate Wilson, and all
of my colleagues at St. Louis Community College, whose
friendship, encouragement and love of mathematics makes
going to work each day a joy.
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Making Connections . . .
Through Supplements
xxvii
*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.
⦁
PowerPoint Slides: Fully editable slides that follow the
textbook.
Student Supplements
⦁
Student Solutions Manual provides comprehensive, worked-out
solutions to all of the odd-numbered exercises.
⦁
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.
www.mhhe.com/coburn
McGraw-Hill’s MathZone is a complete online homework system for
mathematics and statistics. Instructors can assign textbook-specific
content from over 40 McGraw-Hill titles as well as customize the
level of feedback students receive, including the ability to have
students show their work for any given exercise. Assignable content
includes an array of videos and other multimedia along with algorithmic
exercises, providing study tools for students with many different
learning styles.
Within MathZone, a diagnostic assessment tool powered by
ALEKS
®
is available to measure student preparedness and provide
detailed reporting and personalized remediation. MathZone also
helps ensure consistent assignment delivery across several sections
through a course administration function and makes sharing courses
with other instructors easy.
For additional study help students have access to NetTutor™,
a robust online live tutoring service that incorporates whiteboard
technology to communicate mathematics. The tutoring schedules
are built around peak homework times to best accommodate student
schedules. Instructors can also take advantage of this whiteboard
by setting up a Live Classroom for online office hours or a review
session with students.
For more information, visit the book’s website (www.mhhe.com/
coburn) or contact your local McGraw-Hill sales representative
(www.mhhe.com/rep).
www.aleks.com
ALEKS (Assessment and LEarning in Knowledge Spaces) is a
dynamic online learning system for mathematics education, avail-
able over the Web 24/7. ALEKS assesses students, accurately deter-
mines 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.
• Textbook Integration Plus allows ALEKS to be automatically
aligned with syllabi or specified McGraw-Hill textbooks with
instructor chosen dates, chapter goals, homework, and quizzes.
• ALEKS with AI-2 gives instructors increased control over the scope
and sequence of student learning. Students using ALEKS demonstrate
a steadily increasing mastery of the content of the course.
• ALEKS offers a dynamic classroom management system that
enables instructors to monitor and direct student progress towards
mastery of course objectives.
ALEKS Prep/Remediation:
• Helps instructors meet the challenge of remediating unequally
prepared or improperly placed students.
• Assesses students on their pre-requisite knowledge needed for
the course they are entering (i.e. Calculus students are tested on
Precalculus knowledge).
• Based on the assessment, students are prescribed a unique and efficient
learning path specific to address their strengths and weaknesses.
• Students can address pre-requisite knowledge gaps outside of class
freeing the instructor to use class time pursuing course outcomes.
Electronic Textbook: CourseSmart is a new way for faculty to
find and review eTextbooks. It’s also a great option for students who
are interested in accessing their course materials digitally and saving
money. CourseSmart offers thousands of the most commonly
adopted textbooks across hundreds of courses from a wide variety of
higher education publishers. It is the only place for faculty to review
and compare the full text of a textbook online, providing immediate
access without the environmental impact of requesting a print exam
copy. At CourseSmart, students can save up to 50% off the cost of a
print book, reduce their impact on the environment, and gain access
to powerful web tools for learning including full text search, notes
and highlighting, and email tools for sharing notes between classmates.
www.CourseSmart.com
Primis: You can customize this text with McGraw-Hill/Primis
Online. A digital database offers you the flexibility to customize
your course including material from the largest online collection of
textbooks, readings, and cases. Primis leads the way in customized
eBooks with hundreds of titles available at prices that save your
students over 20% off bookstore prices. Additional information is
available at 800-228-0634.
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xxviii
Preface vi
Index of Applications xxxv
CHAPTER R A Review of Basic Concepts and Skills 1
R.1 The Language, Notation, and Numbers of Mathematics 2
R.2 Algebraic Expressions and the Properties of Real Numbers 13
R.3 Exponents, Scientific Notation, and a Review of Polynomials 21
R.4 Factoring Polynomials 35
R.5 Rational Expressions 45
R.6 Radicals and Rational Exponents 55
Overview of Chapter R: Important Definitions, Properties, Formulas,
and Relationships 68
Practice Test 70
CHAPTER 1 Equations and Inequalities 73
1.1 Linear Equations, Formulas, and Problem Solving 74
Technology Highlight: Using a Graphing Calculator as
an Investigative Tool 81
1.2 Linear Inequalities in One Variable 86
1.3 Absolute Value Equations and Inequalities 96
Technology Highlight: Absolute Value Equations and Inequalities 100
Mid-Chapter Check 103
Reinforcing Basic Concepts: Using Distance to Understand
Absolute Value Equations and Inequalities 104
1.4 Complex Numbers 105
1.5 Solving Quadratic Equations 114
Technology Highlight: The Discriminant 123
1.6 Solving Other Types of Equations 128
Summary and Concept Review 142
Mixed Review 147
Practice Test 147
Calculator Exploration and Discovery: Evaluating Expressions and Looking for
Patterns 148
Strengthening Core Skills: An Alternative Method for Checking Solutions to
Quadratic Equations 149
CHAPTER 2 Relations, Functions, and Graphs 151
2.1 Rectangular Coordinates; Graphing Circles and Other Relations 152
Technology Highlight: The Graph of a Circle 160
2.2 Graphs of Linear Equations 165
Technology Highlight: Linear Equations, Window Size, and Friendly Windows 173
2.3 Linear Graphs and Rates of Change 178
2.4 Functions, Function Notation, and the Graph of a Function 190
Mid-Chapter Check 205
Reinforcing Basic Concepts: The Various Forms of a Linear Equation 206
P
Pr
Pr
Pr
ef
ef
f
ace v
i
Contents
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Contents xxix
2.5 Analyzing the Graph of a Function 206
Technology Highlight: Locating Zeroes, Maximums, and Minimums 217
2.6 The Toolbox Functions and Transformations 225
Technology Highlight: Function Families 234
2.7 Piecewise-Defined Functions 240
Technology Highlight: Piecewise-Defined Functions 247
2.8 The Algebra and Composition of Functions 254
Technology Highlight: Composite Functions 264
Summary and Concept Review 270
Mixed Review 277
Practice Test 279
Calculator Exploration and Discovery: Using a Simple Program to Explore
Transformations 280
Strengthening Core Skills: Transformations via Composition 281
Cumulative Review: Chapters 1–2 282
Modeling With Technology I: Linear and Quadratic Equation Models 283
CHAPTER 3 Polynomial and Rational Functions 293
3.1 Quadratic Functions and Applications 294
Technology Highlight: Estimating Irrational Zeroes 299
3.2 Synthetic Division; the Remainder and Factor Theorems 304
3.3 The Zeroes of Polynomial Functions 315
Technology Highlight: The Intermediate Value Theorem
and Split Screen Viewing 325
3.4 Graphing Polynomial Functions 330
Mid-Chapter Check 344
Reinforcing Basic Concepts: Approximating Real Zeroes 344
3.5 Graphing Rational Functions 345
Technology Highlight: Rational Functions and Appropriate Domains 355
3.6 Additional Insights into Rational Functions 362
Technology Highlight: Removable Discontinuities 370
3.7 Polynomial and Rational Inequalities 376
Technology Highlight: Polynomial and Rational Inequalities 383
3.8 Variation: Function Models in Action 389
Summary and Concept Review 399
Mixed Review 404
Practice Test 405
Calculator Exploration and Discovery: Complex Zeroes, Repeated Zeroes,
and Inequalities 407
Strengthening Core Skills: Solving Inequalities Using the Push Principle 407
Cumulative Review: Chapters 1–3 408
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