A GRAPHICAL APPROACH TO COLLEGE ALGEBRA · 2.5 Piecewise-Defined Functions 140 Graphing...

A GRAPHICAL APPROACH TO

COLLEGE ALGEBRASEVENTH EDITION

A01_LIAL9328_07_AIE_FM_i-xx.indd 1 13/10/17 2:24 PM

SAMPLE PREFACE. NOT FOR DISTRIBUTION.

Copyright Pearson. All Rights Reserved.




John Hor nsbyUniversity of New Orleans

Margaret L. LialAmerican River College

Gary RockswoldMinnesota State University, Mankato

with the assistance ofJessica Rockswold

A GRAPHICAL APPROACH TO

COLLEGE ALGEBRASEVENTH EDITION




Director, Portfolio Management: Anne KellyCourseware Portfolio Manager: Chelsea KharakozovaCourseware Portfolio Management Assistant: Ashley GordonContent Producer: Kathleen A. ManleyManaging Producer: Karen WernholmProducer: Marielle GuineyManager, Courseware QA: Mary DurnwaldManager, Content Development: Megan BurnsProduct Marketing Manager: Stacey SveumProduct Marketing Assistant: Shannon McCormackField Marketing Manager: Peggy LucasField Marketing Assistant: Adrianna ValenciaSenior Author Support/Technology Specialist: Joe VetereManager, Rights and Permissions: Gina CheselkaText and Cover Design: Cenveo® Publisher ServicesProduction Coordination, Composition, and Illustrations: Cenveo® Publisher Services

Copyright © 2019, 2015, 2011 by Pearson Education, Inc. All Rights Reserved. Printed in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms, and the appro-priate contacts within the Pearson Education Global Rights & Permissions department, please visit www.pearsoned.com/permissions/.

Attributions of third-party content appear on page C-1, which constitutes an extension of this copyright page.

PEARSON, ALWAYS LEARNING, and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S. and/or other countries.

Unless otherwise indicated herein, any third-party trademarks that may appear in this work are the property of their respective owners and any references to third-party trademarks, logos or other trade dress are for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship, endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner and Pearson Education, Inc. or its affiliates, authors, licensees or distributors.

Library of Congress Cataloging-in-Publication DataNames: Hornsby, John, 1949- author. | Lial, Margaret L., author. | Rockswold, Gary K., author. Title: A graphical approach to college algebra / John Hornsby (University of New Orleans), Margaret L. Lial (American River College), Gary Rockswold (Minnesota State University, Mankato); with the assistance of Jessica Rockswold.Description: Seventh edition. | Boston : Pearson Education, Inc., [2019] | Includes index.Identifiers: LCCN 2017045357 | ISBN 0134696522 (student ed. : alk. paper) |ISBN 0134669320 (annotated instructor’s ed. : alk. paper)Subjects: LCSH: Algebra—Textbooks.Classification: LCC QA152.3 .H67 2019 | DDC 512.9—dc23LC record available at https://lccn.loc.gov/2017045357

1 17

ISBN 13: 978-0-13-469652-2 ISBN 10: 0-13-469652-2

A01_LIAL9328_07_AIE_FM_i-xx.indd 4 03/11/17 11:53 AM



To Susan Danielson




vi

Foreword

The first edition of A Graphical Approach to College Algebra was published in 1996. Our experience was that the usual order in which the standard topics were covered did not foster students’ understanding of the interrelationships among graphs, equations, and inequalities. The table of contents for typical college algebra texts did not allow for maximum effectiveness in implementing our philosophy because graphs were not covered early enough in the course. Thus, we reorganized the standard topics with early introduc-tion to the graphs of functions, followed by solutions of equations, inequalities, and applications. Although

the material is reorganized, we still cover all traditional topics and skills. The underlying theme was, and still is, to illustrate how the graph of a typical function can be used to support the solutions of equations and associated inequalities involving the function.

Using linear functions in Chapter 1 to introduce the approach that follows in later chapters, we apply a four-step process of analysis.

1. We examine the nature of the graph of the function, using both hand-drawn and calculator-generated versions. Domain and range are established, and any further charac-teristics are discussed.

2. We solve equations analytically, using the standard methods. Then we support our solutions graphically, using the intersection-of-graphs method and the x-intercept method (pages 54–55).

3. We solve the associated inequalities analytically, again using standard methodology, supporting their solutions graphically as well.

4. We apply analytic and graphical methods to modeling and traditional applications involving the class of func-tion under consideration.

After this procedure has been initially established for linear functions, we apply it to absolute value, quadratic, higher-degree polynomial, rational, root, exponential, and logarithmic functions in later chap-ters. The chapter on systems of equations ties in the concept of solving systems with the aforementioned intersection-of-graphs method of solving equations.

This presentation provides a sound pedagogical basis. Because today’s students rely on visual learn-ing more than ever, the use of graphs promotes student understanding in a manner that might not occur if only analytic approaches were used. It allows the student the opportunity to see how the graph of a function is related to equations and inequalities involving that function. Students are presented with the same approach over and over, and they come to realize that the type of function ƒ defined by y = ƒ(x) under consideration does not matter when providing graphical support. For example, using the x-intercept method, the student sees that x-values of x-intercepts of the graph of y = ƒ(x) correspond to real solutions of the equation ƒ(x) = 0, x-values of points above the x-axis correspond to solutions of ƒ(x) 7 0, and x-values of points below the x-axis correspond to solutions of ƒ(x) 6 0.

The final result, in conjunction with the entire package of learning tools provided by Pearson, is a course that covers the standard topics of college algebra. It is developed in such a way that graphs are seen as pictures that can be used to interpret analytic results. We hope that you will enjoy teaching this course, and that your students will come away with an appreciation of the impact and importance of our approach in the study of college algebra.

John HornsbyGary Rockswold




Reviewing Basic Concepts (Sections 1.5–1.6) 79

Summary 80

Review Exercises 83

Test 86

Preface xii

1 Linear Functions, Equations, and Inequalities 1

1.1 Real Numbers and the Rectangular Coordinate System 2Sets of Real Numbers • The Rectangular Coordinate System • Viewing Windows • Approximations of Real Numbers • Distance and Midpoint Formulas

1.2 Introduction to Relations and Functions 12Set-Builder Notation and Interval Notation • Relations, Domain, and Range • Functions • Tables and Graphing Calculators • Function Notation


1.3 Linear Functions 23Basic Concepts of Linear Functions • Slope of a Line and Average Rate of Change • Slope–Intercept Form of the Equation of a Line

1.4 Equations of Lines and Linear Models 37Point–Slope Form of the Equation of a Line • Standard Form of the Equation of a Line • Parallel and Perpendicular Lines • Linear Models and Regression


1.5 Linear Equations and Inequalities 50Solving Linear Equations in One Variable • Graphical Approaches to Solving Linear Equations • Identities and Contradictions • Solving Linear Inequalities in One Variable • Graphical Approaches to Solving Linear Inequalities • Compound Inequalities

Unifying Linear Functions 67

1.6 Applications of Linear Functions 68Problem-Solving Strategies • Applications of Linear Equations • Break-Even Analysis • Direct Variation • Formulas

Contents

2 Analysis of Graphs of Functions 88

2.1 Graphs of Basic Functions and Relations; Symmetry 89Continuity • Increasing, Decreasing, and Constant Functions • The Constant and Identity Functions • The Squaring Function and Symmetry with Respect to the y-Axis • The Cubing Function and Symmetry with Respect to the Origin • The Square Root and Cube Root Functions • The Absolute Value Function • The Relation x = y 2 and Symmetry with Respect to the x-Axis • Even and Odd Functions

2.2 Vertical and Horizontal Shifts of Graphs 103Vertical Shifts • Horizontal Shifts • Combinations of Vertical and Horizontal Shifts • Effects of Shifts on Domain and Range • Horizontal Shifts Applied to Equations for Modeling

2.3 Stretching, Shrinking, and Reflecting Graphs 112Vertical Stretching • Vertical Shrinking • Horizontal Stretching and Shrinking • Reflecting across an Axis • Combining Transformations of Graphs


2.4 Absolute Value Functions 126The Graph of y = 0 f (x) 0 • Properties of Absolute Value • Equations and Inequalities Involving Abso-lute Value • Error Tolerances

Unifying Absolute Value Functions 139

vii




viii Contents

2.5 Piecewise-Defined Functions 140Graphing Piecewise-Defined Functions • The Great-est Integer Function • Applications of Piecewise-Defined Functions

2.6 Operations and Composition 153Operations on Functions • The Difference Quotient • Composition of Functions • Composite Functions and Their Domains • Applications of Operations and Composition


Summary 170

Review Exercises 173

Test 176

4 Polynomial Functions of Higher Degree 235

4.1 Graphs of Polynomial Functions 236Basic Terminology • Cubic and Quartic Functions • Extrema • End Behavior • x-Intercepts (Real Zeros) • Comprehensive Graphs • Curve Fitting and Polyno-mial Models

4.2 Topics in the Theory of Polynomial Functions (I) 248Intermediate Value Theorem • Division of Polyno-mials by x − k and Synthetic Division • Remainder and Factor Theorems • Division of Any Two Polynomials


4.3 Topics in the Theory of Polynomial Functions (II) 260Complex Zeros and the Fundamental Theorem of Algebra • Number of Zeros • Rational Zeros Theorem • Descartes’ Rule of Signs • Boundedness Theorem

4.4 Polynomial Equations, Inequalities, Applications, and Models 273Polynomial Equations and Inequalities • Complex nth Roots • Applications and Polynomial Models


Unifying Polynomial Functions 285

Summary 286


Test 291

3 Quadratic Functions 178

3.1 Complex Numbers 179The Imaginary Unit i • Operations with Complex Numbers and Powers of i

3.2 Quadratic Functions and Graphs 186Completing the Square • Graphs of Quadratic Functions • Vertex Formula • Extreme Values • Applications and Quadratic Models • A Quadratic Relation: The Circle


3.3 Quadratic Equations and Inequalities 201Zero-Product Property • Square Root Property and Completing the Square • Quadratic Formula and the Discriminant • Solving Quadratic Equations • Solving Quadratic Inequalities • Formulas Involving Quadratics

Unifying Quadratic Functions 217

3.4 Applications of Quadratic Functions and Models 219Applications of Quadratic Functions • A Quadratic Model


Summary 230


Test 234

5 Rational, Power, and Root Functions 293

5.1 Rational Functions and Graphs (I) 294

The Reciprocal Function, f (x) =1x

• The Reciprocal

of the Square Function, f (x) =1x2

5.2 Rational Functions and Graphs (II) 301Vertical and Horizontal Asymptotes • Graphing Tech-niques • Oblique Asymptotes • Graphs with Points of Discontinuity • Graphs with No Vertical Asymptotes




5.3 Rational Equations, Inequalities, Models, and Applications 318Solving Rational Equations and Inequalities • Models and Applications of Rational Functions • Inverse Variation • Combined and Joint Variation • Rate of Work


Unifying Rational Functions 336

5.4 Functions Defined by Powers and Roots 338Power and Root Functions • Modeling Using Power Functions • Graphs of f (x) = n2ax + b • Graphing Circles and Horizontal Parabolas Using Root Functions

5.5 Equations, Inequalities, and Applications Involving Root Functions 350Equations and Inequalities • An Application of Root Functions


Unifying Root Functions 362

Summary 364


Test 369

6.5 Exponential and Logarithmic Equations and Inequalities 420Exponential Equations and Inequalities (Type 2) • Logarithmic Equations and Inequalities • Equations Involving Exponentials and Logarithms • Formulas Involving Exponentials and Logarithms

Unifying Logarithmic Functions 430

6.6 Further Applications and Modeling with Exponential and Logarithmic Functions 432Physical Science Applications • Financial and Other Applications • Modeling Data with Exponential and Logarithmic Functions


Summary Exercises on Functions: Domains, Defining Equations, and Composition 446Finding the Domain of a Function: A Summary • Determining Whether an Equation Defines y as a Function of x • Composite Functions and Their Domains

Summary 451


Test 458

7 Systems and Matrices 460

7.1 Systems of Equations 461Linear Systems • Substitution Method • Elimination Method • Special Systems • Nonlinear Systems • Applications of Systems

7.2 Solution of Linear Systems in Three Variables 474Geometric Considerations • Analytic Solution of Systems in Three Variables • Applications of Systems • Fitting Data Using a System

7.3 Solution of Linear Systems by Row Transformations 484Matrix Row Transformations • Row Echelon Method (Gaussian Elimination) • Reduced Row Echelon Method • Special Cases • An Application of Matrices


7.4 Matrix Properties and Operations 499Terminology of Matrices • Operations on Matrices • Applying Matrix Algebra

7.5 Determinants and Cramer’s Rule 512Determinants of 2 : 2 Matrices • Determinants of Larger Matrices • Derivation of Cramer’s Rule • Using Cramer’s Rule to Solve Systems

6 Inverse, Exponential, and Logarithmic Functions 371

6.1 Inverse Functions 372Inverse Operations • One-to-One Functions • Inverse Functions and Their Graphs • Equations of Inverse Functions • An Application of Inverse Functions to Cryptography

6.2 Exponential Functions 383Real-Number Exponents • Graphs of Exponential Functions • Exponential Equations (Type 1) • Compound Interest • The Number e and Continuous Compounding • An Application of Exponential Functions

Unifying Exponential Functions 397

6.3 Logarithms and Their Properties 399Definition of Logarithm • Common Logarithms • Natural Logarithms • Properties of Logarithms • Change-of-Base Rule


6.4 Logarithmic Functions 410Graphs of Logarithmic Functions • Finding an Inverse of an Exponential Function • A Logarithmic Model

Contents ix




7.6 Solution of Linear Systems by Matrix Inverses 522Identity Matrices • Multiplicative Inverses of Square Matrices • Using Determinants to Find Inverses • Solving Linear Systems Using Inverse Matrices • Fitting Data Using a System


7.7 Systems of Inequalities and Linear Programming 534Solving Linear Inequalities • Solving Systems of Inequalities • Linear Programming

7.8 Partial Fractions 545Decomposition of Rational Expressions • Distinct Linear Factors • Repeated Linear Factors • Distinct Linear and Quadratic Factors • Repeated Quadratic Factors


Summary 553


Test 559

Summary 604


Test 609

9 Further Topics in Algebra 611

9.1 Sequences and Series 612Sequences • Series and Summation Notation • Summation Properties

9.2 Arithmetic Sequences and Series 622Arithmetic Sequences • Arithmetic Series

9.3 Geometric Sequences and Series 630Geometric Sequences • Geometric Series • Infinite Geometric Series • Annuities


9.4 Counting Theory 640Fundamental Principle of Counting • n-Factorial • Permutations • Combinations • Distinguishing between Permutations and Combinations

9.5 The Binomial Theorem 649A Binomial Expansion Pattern • Pascal’s Triangle • Binomial Coefficients • The Binomial Theorem • r th Term of a Binomial Expansion


9.6 Mathematical Induction 656Proof by Mathematical Induction • Proving Statements • Generalized Principle of Mathematical Induction • Proof of the Binomial Theorem

9.7 Probability 663Basic Concepts • Complements and Venn Diagrams • Odds • Union of Two Events • Binomial Probability


Summary 674


Test 680

8 Conic Sections, Nonlinear Systems, and Parametric Equations 561

8.1 Circles Revisited and Parabolas 562Conic Sections • Equations and Graphs of Circles • Equations and Graphs of Parabolas • Translations of Parabolas • An Application of Parabolas

8.2 Ellipses and Hyperbolas 575Equations and Graphs of Ellipses • Translations of Ellipses • An Application of Ellipses • Equations and Graphs of Hyperbolas • Translations of Hyperbolas


8.3 The Conic Sections and Nonlinear Systems 587Characteristics • Identifying Conic Sections • Eccentricity • Nonlinear Systems

8.4 Introduction to Parametric Equations 598Introduction • Graphs of Parametric Equations and Their Rectangular Equivalents • Alternative Forms of Parametric Equations • An Application of Parametric Equations


R Review: Basic Algebraic Concepts 681

R.1 Review of Sets 682Vocabulary and Symbols • Finite and Infinite Sets • Subsets and Venn Diagrams • Complement of a Set • Union and Intersection of Sets

x Contents




R.2 Review of Exponents and Polynomials 687Rules for Exponents • Terminology for Polynomials • Adding and Subtracting Polynomials • Multiplying Polynomials

R.3 Review of Factoring 693Factoring Out the Greatest Common Factor • Factoring by Grouping • Factoring Trinomials • Factoring Special Products • Factoring by Substitution

R.4 Review of Rational Expressions 699Domain of a Rational Expression • Lowest Terms of a Rational Expression • Multiplying and Divid-ing Rational Expressions • Adding and Subtracting Rational Expressions • Complex Fractions

R.5 Review of Negative and Rational Exponents 707Negative Exponents and the Quotient Rule • Rational Exponents

R.6 Review of Radicals 713Radical Notation • Rules for Radicals • Simplifying Radicals • Operations with Radicals • Rationalizing Denominators

Test 720

Appendix: Formulas from Geometry 723

Answers to Selected Exercises A-1

Photo Credits C-1

Index I-1

Contents xi




xii

Preface

Although A Graphical Approach to College Algebra has evolved significantly from earlier editions, it retains the strengths of those editions and provides new and relevant opportunities for students and instructors alike. We realize that today’s classroom experience is evolving and that technology-based teaching and learning aids have become essential to address the ever-changing needs of instructors and students. As a result, we have worked to provide support for all classroom types—traditional, hybrid, and online. In the seventh edition, text and online materials are more tightly integrated than ever before. This enhances flexibility and ease of use for instructors and increases success for students. See pages xvii–xix for descriptions of these materials.

This text incorporates an open design, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. We continue to offer an Annotated Instructor’s Edition, in which answers to both even- and odd-numbered exercises are provided either beside the exercises (if space permits) or in the back of the text for the instructor.

A Graphical Approach to College Algebra was one of the first texts to reorganize the typical college algebra table of contents to maximize the use of graphs to support solutions of equations and inequalities. It maintains its unique table of contents and functions-based approach (as outlined in the Foreword and in front of the text) and includes additional components to build skills, address critical thinking, and give stu-dents a wealth of opportunities to solve applications and make use of technology to support traditional analytic solutions.

This text is part of a series that also includes the following titles:

●● A Graphical Approach to Algebra and Trigonometry, Seventh Edition, by Hornsby, Lial, and Rockswold

●● A Graphical Approach to Precalculus with Limits: A Unit Circle Approach, Seventh Edition, by Hornsby, Lial, and Rockswold

The book is written to accommodate students who have access to graphing calcula-tors. We have chosen to use screens from the TI-84 Plus C emulator. However, we do not include specific keystroke instructions because of the wide variety of models available. Students should refer to the guides provided with their calculators for spe-cific information.

New to This EditionThere are many places in the text where we have refined individual presentations and added examples, exercises, and applications based on reviewer feedback. The changes you may notice include the following:

●● A NEW recurring feature is titled Unifying Functions. Following discussion of each of the important functions (for example, Unifying Linear Functions on page 67), we present a concise summary that covers Analyzing the Graph, Solving an Equation, Solving an Inequality, and Solving an Application. This feature reinforces the general approach of the text. Accompanying videos are embedded in the eText and assessment questions are available in MyLab Math.




●● Applications have been updated throughout the text in such areas as organic food sales, video-on-demand, active Twitter users, worldwide WhatsApp usage, U.S. Snapchat users, top social networks, wearable technol-ogy, fast-food restaurant and advertising revenue, world records in track, college enrollment, poverty-level income cutoffs, health care expenditures, online sales, online gaming revenue, population, vehicle sales, and pollutant emissions.

●● Graphing calculator screens have been updated using the TI-84 Plus C emulator, often employing pedagogical color.

●● Chapter 1 New Technology Note explaining the equivalence of different function notation styles; updated examples throughout.

●● Chapter 2 More discussion about the constant function; more exercises that determine whether a function is odd or even; additional discussion, examples, and exercises about the order in which to apply combinations of transformations; the difference quotient and average rate of change; com-posite functions and their domains; additional examples of graphical solu-tions to equations and inequalities; a new subsection on error tolerances with examples and exercises; more graphing of absolute value functions by hand; a new example and exercises related to piecewise-defined functions.

(Note: Chapter 3 from the previous edition has been divided into two chapters at the suggestion of reviewers. In the seventh edition, Chapter 3 consists of former Sections 3.1–3.4, and Chapter 4 consists of former Sections 3.5–3.8.)

●● Chapter 3 Additional exercises on quotients of complex numbers; a new subsection on “A Quadratic Relation: The Circle” (this gives the instructor the option to cover circles and completing the square to find the center and radius earlier than in previous editions); new examples and exercises have been added throughout; exercises on complex numbers and exercises on circles have been added to the end-of-chapter Summary and Test.

●● Chapter 4 Introduces the terms upper bound and lower bound; updated examples and exercises appear throughout; additional exercises on polynomial function behavior.

●● Chapter 5 A new example about analyzing graphs of rational functions; new exercises where asymptotes are described using limit notation; new examples and exercises where rational functions are graphed by hand; new examples in which rational inequalities are solved; additional discussion about graphing circles with a calculator; new exercises that involve solving radical inequalities.

●● Chapter 6 Applications of logarithms with bases other than e and 10 have been supplemented with discussion of modern calculator capabilities of computing them directly (the change-of-base rule is still covered); a new example on modeling the number of monthly active Twitter accounts; new discussion, example, and exercises on modeling with logistic functions.

●● Chapter 7 Additional exercises that provide practice in solving systems of equations; more investment examples and applications; new coverage of systems that have infinitely many solutions; many new examples and exer-cises in which systems are solved by hand using row transformations; more discussion and exercises that involve solving rational inequalities; a new example and exercises about partial fraction decomposition.

●● Chapter 8 An example using parametric equations for an object in motion has been expanded; new exercises for parametric graphs have been included.

Preface xiii




xiv Preface

●● Chapter 9 New exercises in solving inequalities that involve both sequences and series; new examples and exercises about mathematical induction; more discussion and exercises about odds in gambling.

●● Chapter R (formerly called “Reference,” now called “Review”) A section on Review of Sets has been added.

FeaturesWe are pleased to offer the following enhanced features:

Chapter Openers Chapter openers provide a chapter outline and a brief discus-sion related to the chapter content.

Enhanced Examples We have replaced some examples and have included many new examples in this edition. We have also polished solutions and incorporated more explanatory comments and pointers.

Hand-Drawn Graphs We have incorporated many graphs featuring a “hand-drawn” style that simulates how a student might actually sketch a graph on grid paper. Accompanying videos are available in the MyLab Math multimedia library.

Dual-Solution Format Selected examples continue to provide side-by-side ana-lytic and graphing calculator solutions, to connect traditional analytic methods for solving problems with graphical methods of solution or support. NEW! Embedded links in the eText enable students to launch a pop-up GeoGebra graphing calculator for these examples (see icon to left).

Pointers Comments with pointers (bubbles) provide students with on-the-spot explanations, reminders, and warnings about common pitfalls.

Highlighted Section and Figure References Within the text we use boldface type when referring to numbered sections and exercises (e.g., Section 2.1, Exercises 15–20). We also use a corresponding font when referring to numbered figures (e.g., FIGURE 1). We thank Gerald M. Kiser of Woodbury (New Jersey) High School for this latter suggestion.

Figures and Photos Today’s students are more visually oriented than ever. As a result, we have made a concerted effort to provide more figures, diagrams, tables, and graphs, including the “hand-drawn” style of graphs, whenever possible. And we often provide photos to accompany applications in examples and exercises.

Function Capsules These special boxes offer a comprehensive, visual introduc-tion to each class of function and serve as an excellent resource for reference and review. Each capsule includes traditional and calculator graphs and a calculator table of values, as well as the domain, range, and other specific information about the func-tion. Abbreviated versions of function capsules are provided on the inside back cover of the text.

What Went Wrong? This popular feature explores errors that students often make when using graphing technology and provides an avenue for instructors to highlight and discuss such errors. Answers are included on the same page as the “What Went Wrong?” boxes. Accompanying videos are available in the MyLab Math multimedia library.




Preface xv

Cautions and Notes These features warn students of common errors and empha-size important ideas throughout the exposition.

Looking Ahead to Calculus These margin notes provide glimpses into how the algebraic topics the students are currently studying are used in calculus.

Algebra Reviews This feature, which appears in the margin of the text, provides “just in time” review by indicating where students can find additional help with important topics from algebra.

Technology Notes Also appearing in the margin, these notes provide tips on how to use graphing calculators more effectively.

Discussing Concepts These activities appear within the exposition or in the margins and offer material on important concepts for instructors and students to inves-tigate or discuss in class.

Exercise Sets We have taken special care to respond to the suggestions of users and reviewers and have added hundreds of new exercises to this edition on the basis of their feedback. The text continues to provide students with ample opportunities to practice, apply, connect, and extend concepts and skills. We have included writing exercises as well as multiple-choice, matching, true/false, and completion prob-lems. Exercises marked CONCEPT CHECK focus on mathematical thinking and concep-tual understanding, while those marked CHECKING ANALYTIC SKILLS are intended to be solved without the use of a calculator.

Relating Concepts These groups of exercises appear in selected exercise sets. They link topics together and highlight relationships among various concepts and skills. All answers to these problems appear in the answer section at the back of the student text.

Reviewing Basic Concepts These sets of exercises appear every two or three sections and give students an opportunity to review and check their understanding of the material in preceding sections. All answers to these problems are included in the answer section.

Chapter Review Material One of the most popular features of the text, each end-of-chapter Summary features a section-by-section list of Key Terms and Symbols, in addition to Key Concepts. A comprehensive set of Chapter Review Exercises and a Chapter Test are also included.

AcknowledgmentsPrevious editions of this text were published after thousands of hours of work, not only by the authors, but also by reviewers, instructors, students, answer checkers, and editors. To these individuals and to all those who have worked in some way on this text over the years, we are most grateful for your contributions. We could not have done it without you.

We especially wish to thank the following individuals who provided valuable input to this and previous editions of the text.

Judy Ahrens, Pellissippi State Technical CollegeRandall Allbritton, Daytona Beach Community

CollegeJamie Ashby, Texarkana CollegeScott E. Barnett, Henry Ford Community College

Gloria Bass, Mercer UniversityPat Bassett, Palm Beach Atlantic UniversityMatthew Benander, Pima Community College, Northwest

CampusKassy Bender, Rowan-Cabarrus Community College




xvi Preface

Daniel Biles, Western Kentucky UniversityLinda Buchanan, Howard CollegeSylvia Calcano, Lake City Community CollegeMegan Cavanah, Polk State College, Lakeland CampusFaye Childress, Central Piedmont Community CollegeMark Crawford, Waubonsee Community CollegeBettyann Daley, University of DelawareSandy Derry, Butler Community CollegeJacqueline Donofrio, Monroe Community CollegePatricia Dueck, Scottsdale Community CollegeMickle Duggan, East Central UniversityDouglas Dunbar, Northwest Florida State CollegeNancy Eschen, Florida Community College at JacksonvilleDonna Fatheree, University of Louisiana at LafayetteNerissa Felder, Polk State College, Lakeland CampusLinda Fosnaugh, Midwestern State UniversityWilliam Frederick, Indiana Purdue University, Fort WayneHenry Graves, Trident Technical CollegeKim Gregor, Delaware Technical Community CollegeSusan Hiatt, Polk State College, Lakeland CampusSandee House, Georgia Perimeter CollegeTeresa Houston, Jackson State UniversityW. H. Howland, University of St. Thomas (Houston)Ana Jimenez, Pima Community CollegeTuesday J. Johnson, New Mexico State UniversityCheryl Kane, University of NebraskaMike Keller, St. John’s River Community CollegeM. R. Khadivi, Jackson State UniversityRosemary Kradel, Lehigh Carbon Community CollegeRachel Lamp, North Iowa Area Community College

Sharon Hawkins MacKendrick, New Mexico State Uni-versity at Grants

Nancy Matthews, University of OklahomaMary Merchant, Cedar Valley CollegeDr. Christian R. Miller, Glendale Community CollegePeggy Miller, University of Nebraska at KearneyPhillip Miller, Indiana University SoutheastStacey McNiel, Lake City Community CollegeRichard Montgomery, The University of ConnecticutLloyd Moyo, Henderson State UniversityMichael Nasab, Long Beach City CollegeJon Odell, Richland Community CollegeKaren Pender, Chaffey CollegeZikica Perovic, Normandale Community CollegeMary Anne Petruska, Pensacola State CollegeSusan Pfeifer, Butler County Community College,

AndoverJohn Putnam, University of Northern ColoradoCharles Roberts, Mercer UniversityDonna Saye, Georgia Southern UniversityAlicia Schlintz, Meredith CollegeLinda K. Schmidt, Greenville Technical CollegeMike Shirazi, Germanna Community CollegeJed Soifer, Atlantic Cape Community CollegeBetty Swift, Cerritos CollegeJulie Tarr, Pima Community CollegeJennifer Walsh, Daytona Beach Community CollegeRobert Woods, Broome Community CollegeFred Worth, Henderson State UniversityKevin Yokoyama, College of the Redwoods

Over the years we have come to rely on an extensive team of experienced professionals at Pearson: Anne Kelly, Chelsea Kharakozova, Kathy Manley, Ashley Gordon, Joe Vetere, Peggy Lucas, Stacey Sveum, Megan Burns, and Marielle Guiney. Thank you to everyone.

We thank Jessica Rockswold, who provided invaluable support and assistance throughout all phases of writing and production. Terry Krieger deserves special rec-ognition for his work with the answers and accuracy checking. Thanks are also due Carol Merrigan for her valuable help as project manager. Finally, we thank Paul Lorczak, Hal Whipple, Dave Atwood, Jack Hornsby, and Mark Rockswold for check-ing answers and page proofs. As an author team, we are committed to providing the best possible text to help instructors teach effectively and help students succeed.

John HornsbyGary Rockswold




MyLab™ Math Online Course for A Graphical Approach to College Algebra 7th edition by Hornsby, Lial, and Rockswold (access code required)

MyLab Math is available to accompany Pearson’s market-leading text offer-ings. To give students a consistent tone, voice, and teaching method, each text’s flavor and approach is tightly integrated throughout the accompanying MyLab Math course, making learning the material as seamless as possible.

Visualization and Conceptual UnderstandingNew! Unifying Functionsfeature appears after the introduction of each of the major classes of functions. It provides a concise summary of the 4-step analytic process that drives this text: Analyze the Graph, Solve an Equa-tion, Solve an Inequality, and Solve a Related Application.

New videos by contributor Jessica Rockswold accompany each instance of Unifying Functions; look for the hotspot in the eText. Assessment questions in MyLab Math allow instructors to assign these videos and test conceptual under-standing.

New! Example Solution Videosengage and support students outside the class-room while covering key topics hand-picked by the authors. Lightboard technology creates a personal experience and simulates an in-class environment. Accompanying assessment questions in MyLab Math make these brand new videos assignable.

pearson.com/mylab/math

xvii




Guided Visualizationsbring mathematical concepts to life, helping students visualize the concepts through direct-ed explorations and purposeful manipulation. Guided Visualizations can be assigned in MyLab Math to encourage active learning, critical think-ing, and conceptual understanding.

Student MotivationLearning Catalyticsgenerate class discussion, guide your lecture, and promote peer-to-peer learning with real-time analytics. MyLab Math now provides Learning Catalytics—an interactive student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking.Instructors, you can:

• Pose a variety of open-ended questions that help your students develop critical thinking skills

• Monitor responses to find out where students are struggling

• Use real-time data to adjust your instructional strategy and try other ways of engaging your students during class

• Manage student interactions by automatically grouping stu-dents for discussion, teamwork, and peer-to-peer learning

New! GeoGebra® Graphing Calculator and Tutorials

support Hornsby’s graphical approach. GeoGebra, an online graphing utility, is integrated into the MyLab Math course. Look for the GeoGebra icon within the eText to open a pop-up version, deploy in a new browser tab from Graphing Resources, or download the free app to use while doing homework. Interactive, self-checking tutorials make it easy to get started with this dynamic tool.


xviii




Instructor ResourcesThese additional resources can be downloaded from www.pearson.com or from within your MyLab Math course.

Annotated Instructor’s EditionThis edition provides answers beside the text where possible for quick reference and in an answer sec-tion at the back of the book for all others.

Instructor’s Solutions ManualThis manual provides complete solutions to all text exercises.

TestGen®

TestGen (www.pearsoned.com/testgen) enables in-structors to build, edit, print, and administer tests using a computerized bank of questions developed to cover all the objectives of the text.

PowerPoint® Lecture SlidesThe PowerPoint lecture slides feature presentations written and designed specifically for this text, in-cluding figures and examples from the text.

Instructor’s Testing ManualBy David Atwood, Rochester Community and Techni-cal CollegeThis testing manual contains four alternative tests for each chapter and corresponding answer keys.

Student Activities GuidesBy Susan FifeThis guide contains answers to Precalculus Activities using WolframAlpha™ and Engaging Algebra: Activities that Create Connections.

Sample Assignments in MyLab MathEnhanced Sample Assignments, created by the authors, make course set-up easier by giving in-structors a starting point for each chapter. Each as-signment, handpicked by the author team to align with this text, includes a thoughtful mix of question

types (e.g., conceptual, skills, etc.) specific to that topic. Each assignment includes the newest MyLab Math question types including video assessments and guided visualizations.

Learning CatalyticsGenerate class discussion, guide your lecture, and promote peer-to-peer learning with real-time analyt-ics. MyLab Math now provides Learning Catalytics—an interactive student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking.

Student ResourcesThese additional resources promote student success.

Student’s Solutions ManualThis manual provides detailed solutions to odd-numbered Section and Chapter Review Exercises, as well as to all Relating Concepts, Reviewing Basic Concepts, and Chapter Test problems.

Video ProgramExample Solution videos provide comprehensive coverage of key topics in the text in an engaging for-mat. Unifying the Function videos summarize the 4-step solving process featured throughout the text-book for each of the major classes of functions. All videos are assignable in MyLab Math and available in the Multimedia Library.

Graphing ResourcesInteractive tutorials and how-to videos are available for GeoGebra and TI-84 Plus, respectively. These resources and more can be found in the Graphing Resources tab in MyLab Math. Students will be able to launch the GeoGebra graphing calculator from that tab, within their eText, or by downloading the free app to use while completing assignments.

Resources for Success


xix







Date post:	14-Sep-2019
Category:	Documents
Upload:	others
View:	53 times
Download:	1 times

A GRAPHICAL APPROACH TO COLLEGE ALGEBRA · 2.5 Piecewise-Defined Functions 140 Graphing...

Documents