PREFACE

xi

Our Mission

The goal of College Algebra and Trigonometry: Building Concepts and Connections is toteach students to more clearly see how mathematical concepts connect and relate.Weset out to accomplish this goal in two fundamental ways.

Functions as a Unifying ThemeFirst, we considered the order in which functions should be presented relative to theircorresponding equations. Accordingly, rather than present a comprehensive review ofequations and equation solving in Chapter 1, we introduce functions in Chapter 1.Wethen present related equations and techniques for solving those equations in the con-text of their associated functions. When equations are presented in conjunction withtheir “functional” counterparts in this way, students come away with a more coherentpicture of the mathematics.

Pedagogical ReinforcementWe also created a pedagogy that “recalls” previous topics and skills by way of linkedexamples and Just in Time exercises and references. Through these devices, studentsreceive consistent prompts that enable them to better remember and apply what theyhave learned.

Ultimately, our hope is that through College Algebra and Trigonometry: Building Conceptsand Connections, students will develop a better conceptual understanding of the sub-ject and achieve greater preparedness for future math courses.

Which Textbook is Right for You?We recognize that instructors’ needs in this course area are diverse. By offering varia-tion in the coverage of trigonometry—in particular, variation in the right triangle ap-proach relative to the unit circle approach—this series strives to meet everyone’s needs.

College Algebra and Trigonometry: Building Concepts and Connections

Do you put as much emphasis on the right triangle ap-proach as you do the unit circle approach to find thevalues of trigonometric functions of non-acute angles?

If so, we recommend College Algebra and Trigonometry.

Precalculus: Building Concepts and Connections

Do you emphasize use of the unit circle to find the val-ues of trigonometric functions of non-acute angles,more so than the right triangle approach?

If so, we recommend Precalculus.

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xi

Right Triangle Approach versus Unit Circle Approach: A Closer LookIn Chapter 6 of College Algebra and Trigonometry the author includes two sections onright triangle trigonometry (Sections 6.2 and 6.3), that covers all angles, as well as asection on the unit circle (Section 6.4), that also covers all angles.

In Precalculus, the author includes one section on right triangle trigonometry (Sec-tion 5.2), focusing on acute angles, and one on the unit circle approach, (Section 5.3),that covers all angles.

Whichever title you choose, you and your students will benefit from clear, com-prehensive instruction and innovative pedagogy that are synonymous with the series.

Instruction and Pedagogy

The instruction and pedagogy have been designed to help students make greater senseof the mathematics and to condition good study habits. We endeavor to keep studentsengaged, to help them make stronger connections between concepts, and to encour-age exploration and review on a regular basis.

EngageContemporary and Classical Applications Applications are derived from a wide varietyof topics in business, economics, and the social and natural sciences. While moderndata is well represented, classical applications are also infused in various exercise setsand examples. Integrating applications throughout the text improves the accessibility ofthe writing by providing a firm context. It also helps students to develop a strongersense of how mathematics is used to analyze problems in a variety of disciplines, to drawcomparisons between discrete sets of data, and to make more informed decisions.

Writing Style We make every effort to write in an “open” and friendly manner to re-duce the intimidation sometimes experienced by students when reading a mathemat-ics textbook. We provide patient explanations while maintaining the mathematicalrigor expected at this level. We also reference previously-introduced topics when ap-propriate, to help students draw stronger links between concepts. In this way, we hopeto keep students more engaged and promote their success when working outside theclassroom.

ConnectJust in Time References These references are found in the margins throughout thetextbook, where appropriate. They point to specific pages within the textbook wherethe referenced topics were first introduced and thus enable students to quickly turnback to the original discussions of the cited topics.

Just in Time Exercises These exercises are included as the first set of exercises at theend of many sections.These exercises correlate to the Just in Time references that ap-pear within the section. They are provided to help students recall what they have pre-viously learned for direct application to new concepts presented in the current section.

Repeated Themes We frequently revisit examples and exercises to illustrate how ideas may be advanced and extended. In particular, certain examples, called LinkedExamples, have been labeled with l icons so that instructors and students can con-nect them with other examples in the book. Through these devices, students can syn-thesize various concepts and skills associated with a specific example or exercise topic.

xii ■ Preface

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xii

ExploreKeystroke Appendix A Keystroke Appendix for the TI-83/84 family of calculators is in-cluded at the end of the book for quick reference. The appendix contents parallel theorder of topics covered in the textbook and offer detailed instruction on keystrokes,commands, and menus.

Technology Notes Technology Notes appear in the margins to support the optional use of graphing calculator technology and reference the Keystroke Appendix when ap-propriate. The screen shots and instructions found within the Technology Notes havebeen carefully prepared to illustrate and support some of the more subtle details ofgraphing calculator use that can often be overlooked.

Discover and Learn These instructor-guided exercises appear within the discussions ofselected topics. They are designed as short, in-class activities and are meant to en-courage further exploration of the topic at hand.

Review and ReinforceChapter P Chapter P has been developed for students or instructors who want to re-view prerequisite skills for the course. Topics include the real number system; expo-nents and scientific notation; roots, radicals, and rational exponents; polynomials;factoring; rational expressions; geometry; and rudimentary equation-solving.

Check It Out A Check It Out exercise follows every example. These exercises providestudents with an opportunity to try a problem similar to that given in the example.Theanswers to each Check It Out are provided in an appendix at the back of the textbookso that students can immediately check their work and self-assess.

Observations Observations appear as short, bulleted lists that directly follow thegraphs of functions.Typically, the Observations highlight key features of the graphs offunctions, but they may also illustrate patterns that can help students organize theirthinking. Since Observations are repeated throughout the textbook, students will getinto the habit of analyzing key features of functions. In this way, the Observations willcondition students to better interpret and analyze what they see.

Notes to the Student Placed within the exposition where appropriate, the Notes pro-vide tips on avoiding common errors or offer further information on the topic underdiscussion.

Key Points At the end of every section, the Key Points summarize major themes fromthe section. They are presented in bullet form for ease of use.

Three-Column Chapter Summary A detailed Summary appears at the end of every chap-ter. It is organized by section and illustrates the main concepts presented in each sec-tion. Examples are provided to accompany the concepts, along with references toexamples or exercises within the chapter. This format helps students quickly identifykey problems to practice and review, ultimately leading to more efficient study sessions.

Preface ■ xiii

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xiii

Additional Resources

xiv ■ Preface

INSTRUCTOR RESOURCES STUDENT RESOURCES

Instructor’s Annotated Edition (IAE)—a replica ofthe student textbook with answers to all exercises either embedded within the text pages or given in the Instructor Answer Appendix at the back of thetextbook.

Student Solutions Manual—a manual containingcomplete solutions to all odd-numbered exercises andall of the solutions to the Chapter Tests.

HM Testing (Powered by Diploma™)—acomputerized test bank that offers a wide array ofalgorithms. Instructors can create, author/editalgorithmic questions, customize, and deliver multipletypes of tests.

Instructional DVDs—Hosted by Dana Mosley, these DVDs cover all sections of the text and provideexplanations of key concepts in a lecture-based format. DVDs are closed-captioned for the hearing-impaired.

For more information, visit college.hmco.com/pic/narasimhanCAT1e or contactyour local Houghton Mifflin sales representative.

HM MathSPACE® encompasses the interactive online products and services integrated with Houghton Mifflin textbook programs. HM MathSPACE is available through text-specific student and instructorwebsites and via Houghton Mifflin’s online course management system. HM MathSPACE includes homeworkpowered by WebAssign®; a Multimedia eBook; self-assessment and remediation tools; videos, tutorials, andSMARTHINKING®.

� WebAssign®—Developed by teachers, for teachers, WebAssign allows instructors to create assignments from an abundant ready-to-use database of algorithmic questions, or write and customize their own exercises. With WebAssign, instructors can create, post, and review assignments 24 hours a day, 7 days a week; deliver, collect,grade, and record assignments instantly; offer more practice exercises, quizzes, and homework; assess student per-formance to keep abreast of individual progress; and capture the attention of online or distance learning students.

� Online Multimedia eBook—Integrates numerous assets such as video explanations and tutorials to expandupon and reinforce concepts as they appear in the text.

� SMARTHINKING® Live, Online Tutoring—Provides an easy-to-use and effective online, text-specific tutoringservice. A dynamic Whiteboard and a Graphing Calculator function enable students and e-structors to collaborateeasily.

� Student Website—Students can continue their learning here with a multimedia eBook, glossary flash cards, andmore.

� Instructor Website—Instructors can download solutions to textbook exercises via the Online Instructor’s Solu-tions Manual, digital art and figures, and more.

Powerful online tools. Premium content.

Online Course Management Content for Blackboard®, WebCT®, and eCollege®—Deliver program- or text-specific Houghton Mifflin content online using your institution’s local course management system. HoughtonMifflin offers homework, tutorials, videos, and other resources formatted for Blackboard, WebCT, eCollege, andother course management systems. Add to an existing online course or create a new one by selecting from a widerange of powerful learning and instructional materials.

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xiv

Acknowledgments

We would like to thank the following instructors and students who participated in thedevelopment of this textbook. We are very grateful for your insightful comments anddetailed review of the manuscript.

Manuscript Reviewers and Other Pre-Publication Contributors

Preface ■ xv

April AllenBaruch College

Carolyn Allred-WinnettColumbia State Community College

Jann AveryMonroe Community College

Rich AveryDakota State University

Robin L. AyersWestern Kentucky University

Donna J. BaileyTruman State University

Andrew BalasUniversity of Wisconsin, Eau Claire

Michelle BenedictAugusta State University

Marcelle BessmanJacksonville University

Therese BlynWichita State University

Bill BonnellGlendale Community College

Beverly BroomellSuffolk County Community College

Bruce BurdickRoger Williams University

Veena ChadhaUniversity of Wisconsin, Eau Claire

Mark D. ClarkPalomar College

Jodi CottenWestchester Community College

Anne DarkeBowling Green State University

Amit DaveDekalb Technical Institute

Luz De AlbaDrake University

Kamal DemianCerritos College

Tristan DenleyUniversity of Mississippi

Deborah Denvir,Marshall University

Richard T. DriverWashburn University

Douglas DunbarOkaloosa Walton Community College

Royetta EalbaHenry Ford Community College

Carolyn EdmondUniversity of Arizona

C. Wayne EhlerAnne Arundel Community College

Donna FathereeUniversity of Louisiana, Lafayette

Kevin A. FoxShasta College

Jodie FryBroward Community College

Cathy GardnerGrand Valley State University

Don GibbonsRoxbury Community College

Dauhrice K. GibsonGulf Coast Community College

Gregory GibsonNorth Carolina A & T StateUniversity

Irie GlajarAustin Community College

Dr. Deborah L. GochenaurElizabethtown College

Sara GoldammerUniversity of South Dakota

Scott GordonThe University of West Georgia

Patricia GramlingTrident Technical College

Michael GreenwichCommunity College of SouthernNevada

Robert GriffithsMiami Dade College, Kendall

David GrossUniversity of Connecticut

Margaret GruenwaldUniversity of Southern Indiana

Brian Karl HagelstromNorth Dakota State–College of Science

Shirley HagewoodAustin Peay State University

Shawna HaiderSalt Lake Community College

Cheri J. HarrellNorth Carolina Central University

Mako HarutaUniversity of Hartford

Andrea HendricksGeorgia Perimeter College

Jada HillRichland Community College

Gangadhar HiremathUniversity of North Carolina, Pembroke

Eric HofackerUniversity of Wisconsin–River Falls

Thomas HoffmanCoastal Carolina University

Lori HoldenManatee Community College

Eric HsuSan Francisco State University

Charlie HuangMcHenry County College

Rebecca HubiakTidewater Community College,Virginia Beach

Jennifer JamesonCoconino County Community College

Larry Odell JohnsonDutchess Community College

Tina JohnsonMidwestern State University

Michael J. KantorUniversity of Wisconsin, Madison

Dr. Rahim G. KarimpourSouthern IllinoisUniversity–Edwardsville

Mushtaq KhanNorfolk State University

Helen KolmanCentral Piedmont Community College

Tamela KostosMcHenry County College

Linda KuroskiErie Community College

Marc LamberthNorth Carolina A&T State University

Charles G. LawsCleveland State Community College

Dr. William LiuBowling Green StateUniversity–Firelands College

Matt LunsfordUnion University

Jo MajorFayetteville Technical CommunityCollege

Kenneth MannCatawba Valley Community College

Mary Barone MartinMiddle Tennessee State University

Dave MatthewsMinnesota West Community andTechnical College

Marcel MaupinOklahoma State University,Oklahoma City

Joe MayNorth Hennepin Community College

Melissa E. McDermidEastern Washington University

Mikal McDowellCedar Valley College

Terri MillerArizona State University

Ferne MizellAustin Community College, Rio Grande

Shahram NazariBauder College

Katherine NicholsUniversity of Alabama

Lyn NobleFlorida Community College, South

Tanya O’ KeefeDarton College, Albany

Susan PaddockSan Antonio College

Carol PaxtonGlendale College

Dennis PenceWestern Michigan University

Nancy PeveyPellissippi State Technical CommunityCollege

Jane PinnowUniversity of Wisconsin, Parkside

David PlattFront Range Community College

Margaret PoitevintNorth Georgia College

Julia PolkOkaloosa Walton Community College

Jennifer PowersMichigan State University

Anthony PrecellaDel Mar College

Ken PrevotMetro State College, Denver

Laura PyzdrowskiWest Virginia University

Bala RahmanFayetteville Technical CommunityCollege

Jignasa RamiCommunity College Baltimore County,Catonsville

Margaret RamseyChattanooga State TechnicalCommunity College

Richard RehbergerMontana State University

David RoachMurray State University

Dan RotheAlpena Community College

Haazim SabreeGeorgia Perimeter College

Radha SankaranPassaic County Community College

Cynthia SchultzIllinois Valley Community College

Shannon SchumannUniversity of Colorado, Colorado Springs

Bethany SetoHorry-Georgetown Technical College

Edith SilverMercer County Community College

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xv

xvi ■ Preface

Dean BarchersRed Rocks Community College

Steven CastilloLos Angeles Valley College

Diedra CollinsGlendale Community College

Rohan DalpataduUniversity of Nevada, Las Vegas

Mahmoud El-HashashBridgewater State College

Angela EverettChattanooga State TechnicalCommunity College

Brad FeldserKennesaw State University

Eduardo GarciaSanta Monica Community CollegeDistrict

Lee GraubnerValencia Community College

Barry GriffithsUniversity of Central Florida

Dan HarnedLansing Community College

Brian HonsSan Antonio College

Grant KaramyanUniversity of California, Los Angeles

Paul Wayne LeeSt. Philips College

Richard Allen LeedyPolk Community College

Aaron LevinHolyoke Community College

Austin LovensteinPulaski Technical College

Janice LyonTallahassee Community College

Jane MaysGrand Valley State University

Barry MonkMacon State College

Sanjay MundkurKennesaw State University

Kenneth PothovenUniversity of South Florida

Jeff RushallNorthern Arizona University

Stephanie SibleyRoxbury Community College

Jane SmithUniversity of Florida

Joyce SmithChattanooga State TechnicalCommunity College

Jean ThortonWestern Kentucky University

Razvan VerzeanuFullerton College

Thomas WelterBethune Cookman College

Steve WhiteJacksonville State University

Bonnie Lou WicklundMount Wachusett Community College

Don WilliamsonChadron State College

Mary D. WolfeMacon State College

Maureen WoolhouseQuinsigamond Community College

Focus Group Attendees

Irina AndreevaWestern Illinois University

Richard AndrewsFlorida A&M University

Mathai AugustineCleveland State Community College

Laurie BattleGeorgia College & State University

Sam BazziHenry Ford Community College

Chad BemisRiverside Community College District

Rajeed CarrimanMiami Dade College, North

Martha M. ChalhoubCollin County Community College

Tim ChappellPenn Valley Community College

Oiyin Pauline ChowHarrisburg Area Community College

Allan DanuffCentral Florida Community College

Ann DarkeBowling Green State University

Steven M. DavisMacon State College

Jeff DoddJacksonville State University

Jennifer DuncanManatee Community College

Abid ElkhaderNorthern State University

Nicki FeldmanPulaski Technical College

Perry GillespieFayetteville State University

Susan GrodyBroward Community College

Don GroningerMiddlesex County College

Martha HaehlPenn Valley Community College

Katherine HallRoger Williams University

Allen C. HamlinPalm Beach Community College, Lake Worth

Celeste HernandezRichland College

Lynda HollingsworthNorthwest Missouri State University

Sharon HolmesTarrant County College

David HopePalo Alto College

Jay JahangiriKent State University

Susan JordanArkansas Technical University

Rahim G. KarimpourSouthern Illinois University,Edwardsville

William KeigherRutgers University, Newark

Jerome KrakowiakJackson Community College

Anahipa LorestaniSan Antonio College

Cyrus MalekCollin County Community College

Jerry MayfieldNorthlake College

M. Scott McClendonUniversity of Central Oklahoma

Francis MillerRappahannock Community College

Sharon MorrisonSt. Petersburg College

Adelaida QuesadaMiami Dade College, Kendall

Sondra RoddyNashville State Community College

Randy K. RossMorehead State University

Susan W. SabrioTexas A&M University, Kingsville

Manuel SandersUniversity of South Carolina

Michael SchroederSavannah State University

Mark SigfridsKalamazoo Valley Community College

Mark StevensonOakland Community College

Pam StogsdillBossier Parish Community College

Denise SzecseiDaytona Beach Community College

Dr. Katalin SzucsEast Carolina University

Mahbobeh VezvaeiKent State University

Lewis J. WalstonMethodist University

Jane-Marie WrightSuffolk County Community College

Tzu-Yi Alan YangColumbus State Community College

Marti ZimmermanUniversity of Louisville

Class Test Participants

Randy SmithMiami Dade College

Jed SoiferAtlantic Cape Community College

Donald SolomonUniversity of Wisconsin, Milwaukee

Dina SpainHorry-Georgetown Technical College

Carolyn SpillmanGeorgia Perimeter College

Peter StaabFitchburg State College

Robin SteinbergPima Community College

Jacqui StoneUniversity of Maryland

Clifford StoryMiddle Tennessee State University

Scott R. SykesState University of West Georgia

Fereja TahirIllinois Central College

Willie TaylorTexas Southern University

Jo Ann TempleTexas Tech University

Peter ThielmanUniversity of Wisconsin, Stout

J. Rene TorresUniversity of Texas-Pan American

Craig TurnerGeorgia College & State University

Clen VanceHouston Community College, Central

Arun K. Verma, Ph.D.Hampton University

Susan A. WalkerMontana Tech, The University ofMontana

Barrett WallsGeorgia Perimeter College

James L. WangUniversity of Alabama

Fred WarnkeUniversity of Texas, Brownsville

Carolyn WarrenUniversity of Mississippi

Jan WehrUniversity of Arizona

Richard WestFrancis Marion University

Beth WhiteTrident Technical College

Jerry WilliamsUniversity of Southern Indiana

Susan WillifordColumbia State Community College

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xvi

Olutokumbo AdebusuyiFlorida A&M University

Jeremiah AdueiFlorida A&M University

Jennifer AlbornozBroward Community College, North

Steph AllisonBowling Green State University

Denise AndersonDaytona Beach Community College

Aaron AndersonDaytona Beach Community College

India Yvette AndersonJacksonville State University

Sharon AugusteBroward Community College, North

Danielle AultJacksonville State University

Genisa Autin-HollidayFlorida A&M University

Dylan BakerSaint Petersburg College

Mandie BaldwinBowling Green State University

Heather BalsamoCollin County Community College,Spring Creek

Emmanuel BarkerDaytona Beach Community College

Nataliya V. BattlesArkansas Tech University

Jason BeardsleeNorth Lake College

Barbara BelizaireBroward Community College, North

Akira BenisonJacksonville State University

Derek S. BentKalamazoo Valley Community College

Janice BerbridgeBroward Community College, North

Corey BieberJackson Community College

Michael BieglerNorthern State University

Robert BogleFlorida A&M University

Skyy BondFlorida A&M University

Brittany BradleyArkansas Tech University

Josh BraunNorthern State University

Marcus BrewerManatee Community College

Jeniece BrockBowling Green State University

Channing BrooksCollin County Community College,Spring Creek

Renetta BrooksFlorida A&M University

Jonathan BrownArkansas Tech University

Jawad BrownFlorida A&M University

Ray BrownManatee Community College

Jill BungeBowling Green State University

Melissa BussNorthern State University

Kimberly CalhounJacksonville State University

Joshua CamperNorthern State University

Andrew CaponeFranklin and Marshall

Bobby CarawayDaytona Beach Community College

Brad CarperMorehead State University

Megan ChampionJacksonville State University

Kristen ChapmanJacksonville State University

Shaina ChesserArkansas Tech University

Alisa ChirochanapanichSaint Petersburg College

Holly CobbJacksonville State University

Travis ColemanSaint Petersburg College

Jazmin ColonMiami Dade College, North

Stephen ColuccioSuffolk County Community College

Cynthia Y. CorbettMiami Dade College, North

Maggie CoyleNorthern State University

Theresa CraigBroward Community College, North

Elle CroftonRutgers University

Shanteen DaleyFlorida A&M University

Joann DeLuciaSuffolk County Community College

Christopher DeneenSuffolk County Community College

William DengNorthern State University

Erica DerreberryManatee Community College

Brendan DiFerdinandDaytona Beach Community College

Rathmony DokNorth Lake College

Julie EatonPalm Beach Community College

Courtnee EddingtonFlorida A&M University

Shaheen EdisonFlorida A&M University

Jessica EllisJacksonville State University

Deborah J. EllisMorehead State University

Victoria EnosKalamazoo Valley Community College

Amber EvangelistaSaint Petersburg College

Ruby ExantusFlorida A&M University

Staci FarnanArkansas Tech University

Falon R. FentressTarrant County College, Southeast

Kevin FinanBroward Community College, North

Daniela FlinnerSaint Petersburg College

Shawn FloraMorehead State University

Lisa ForrestNorthern State University

Ryan FrankartBowling Green State University

Ashley FrystakBowling Green State University

Desiree GarciaJacksonville State University

Benjamin GarciaNorth Lake College

Josie GarciaPalo Alto College

Jahmal GarrettBowling Green State University

Robyn GeigerKalamazoo Valley Community College

Melissa GentnerKalamazoo Valley Community College

James GillespieUniversity of Louisville

Jeanette GlassCollin County Community College,Spring Creek

Holly GonzalezNorthern State University

Jennifer GorsuchJackson Community College

Josh GovanArkansas Tech University

Lindsey GraftJacksonville State University

Sydia GrahamBroward Community College, North

Donald R. Gray IIIMorehead State University

Melissa GreeneBowling Green State University

Stacy HaenigSaint Petersburg College

Mitchell HaleyMorehead State University

Seehee HanSan Antonio College

Kimberly HarrisonJacksonville State University

Emily Diane HarrisonMorehead State University

Joshua HayesSan Antonio College

Leeza HeavenMiami Dade College, North

David HeinzenArkansas Tech University

Katrina HendersonJacksonville State University

Ashley HendrySaint Petersburg College

Johnathan HentschelArkansas Tech University

Amber HicksJacksonville State University

Ryan HilgemannNorthern State University

Maurice HillmanBowling Green State University

Matt HobeJackson Community College

Neda HosseinyNorth Lake College

Laura HydenBowling Green State University

Blake JacksonJacksonville State University

David JaenNorth Lake College

K. C. JanssonCollin County Community College,Spring Creek

Wesley JenningsNorthern State University

Racel JohnsonCollin County Community College,Spring Creek

Kevin JonesMiami Dade College, North

Matt KalkbrennerPulaski Technical College

Brenda KohlmanNorthern State University

Tanya KonsDaytona Beach Community College

Kevin LaRose-RennerDaytona Beach Community College

Alex David LasurdoSuffolk County Community College

Amber LeeJacksonville State University

Amanda LipinskiNorthern State University

Ryan LipsleyPulaski Technical College

Amber LoganFlorida A&M University

Chris LundgrenMiami Dade College, North

Lindsay LvensKalamazoo Valley Community College

Student Class Test Participants

Preface ■ xvii

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xvii

Lisa MainzPalo Alto College

Patricia MantoothJacksonville State University

Jaclyn MargolisSuffolk County Community College

Summer MartinJacksonville State University

Miguel MartinezSan Antonio College

Ali MasumiCollin County Community College,Spring Creek

Somer Dawn MatterSaint Petersburg College

Tiffany MauriquezCollin County Community College,Spring Creek

Tania MaxwellDaytona Beach Community College

Durya McDonaldFlorida A&M University

Bekah McCarleyArkansas Tech University

W. McLeodJackson Community College

Shannon McNealMorehead State University

Carolina MedinaTarrant County College, Southeast

Lilliam MercadoMiami Dade College, North

Chelsea MetcalfNorth Lake College

John H. MeyerUniversity of Louisville

Christina MichlingCollin County Community College,Spring Creek

Chris MiggeNorthern State University

Della MitchellFlorida A&M University

Debra MogroMiami Dade College, North

Emily MohneyKalamazoo Valley Community College

Demaris MoncadaMiami Dade College, North

Kathleen MonkJackson Community College

Virginia MoraPalo Alto College

James MoralesSan Antonio College

Amber MorganJacksonville State University

Justin MurrayBowling Green State University

Ernesto Noguera GarcíaJacksonville State University

Courtney NullJacksonville State University

Gladys OkoliNorth Lake College

Ashley OlivierSan Antonio College

Jonathan OrjuelaDaytona Beach Community College

Lucia OrozcoMiami Dade College, North

Elizabeth PatchakKalamazoo Valley Community College

Natasha PatelSan Antonio College

Braden PetersonCollin County Community College,Spring Creek

Jenny PhillipsNorthern State University

Karina PierceFayetteville State University

Joe PietrafesaSuffolk County Community College

Lacie PineKalamazoo Valley Community College

Brandon PisacritaJacksonville State University

Andrea PrempelTarrant County College, Southeast

Kaylin PurcellDaytona Beach Community College

Mary Michelle QuillianJacksonville State University

Elizabeth QuinliskSaint Petersburg College

Kristina RandolphFlorida A&M University

Ian RawlsFlorida A&M University

Heather RayburgManatee Community College

Samantha RenoArkansas Tech University

Marcus RevillaSan Antonio College

Kyle RosenbergerBowling Green State University

Cassie RowlandKalamazoo Valley Community College

Jason RussellJacksonville State University

Brian P. RzepaManatee Community College

Matt SandersonArkansas Tech University

Ana SantosDaytona Beach Community College

Allison SchachtBowling Green State University

Dwayne ScheunemanSaint Petersburg College

Jacqueline SchmidtNorthern State University

Danielle SerraSuffolk County Community College

Kelly LeAnn SheltonMorehead State University

Naomi ShoemakerPalo Alto College

Chelsey SiebrandsNorthern State University

Justin SilviaTarrant County College, Southeast

Bethany SingreyNorthern State University

Eron SmithArkansas Tech University

Klye SmithJackson Community College

Nicholas SolozanoCollin County Community College,Spring Creek

Joslyn SorensenManatee Community College

Hailey StimpsonPalo Alto College

Yanti SunggonoPulaski Technical College

Sharne SweeneyFayetteville State University

Katherine SweigartArkansas Tech University

Amanda TewksburyNorthern State University

Jenna ThomsonManatee Community College

Diego F. TorresSan Antonio College

Tiffany TrumanManatee Community College

Alice TurnboMorehead State University

Anselma Valcin-GreerBroward Community College, North

A’Donna WaferBowling Green State University

Christy WardOhio University

Portia WellsDaytona Beach Community College

Larissa WessBowling Green State University

Ben WhiteFlorida A&M University

Theresa WilliamsSuffolk County Community College

Amy WislerBowling Green State University

Aikaterini XenakiDaytona Beach Community College

Kristen YatesMorehead State University

Amanda YoungManatee Community College,Bradenton

Stephanie ZinterNorthern State University

Kristen ZookCollin County Community College,Spring Creek

xviii ■ Preface

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xviii

In addition, many thanks to Georgia Martin, who provided valuable feedback on theentire manuscript. Also, thanks to Brenda Burns, Noel Kamm, Joan McCarter, RekhaNatarajan, Danielle Potvin, George Pasles, Sally Snelson, and Douglas Yates for their assistance with the manuscript and exercise sets; Carrie Green, Lauri Semarne, andChristi Verity for accuracy reviews; Mark Stevenson for writing the solutions manuals;and Dana Mosely for the videos.

At Houghton Mifflin, I wish to thank Erin Brown and Molly Taylor for taking spe-cial care in guiding the book from its manuscript stages to production; Jennifer Jonesfor her creative marketing ideas; Tamela Ambush for superbly managing the produc-tion process; and Richard Stratton for his support of this project.

Special thanks to my husband, Prem Sreenivasan, our children, and our parents fortheir loving support throughout.

Preface ■ xix

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xix

� Section ObjectivesEach section begins with a list of bulleted objectives offering an at-a-glance overview of what will be covered.

ChapterOpener �

Each Chapter Openerincludes an applied ex-ample of content thatwill be introduced inthe chapter. An outline of the sectionprovides a clear pictureof the topics beingpresented.

213

C h a p t e r

33.1 Graphs of QuadraticFunctions 214

3.2 Quadratic Equations231

3.3 Complex Numbersand Quadratic Equations

246

3.4 QuadraticInequalities 256

3.5 Equations That AreReducible to QuadraticForm; Rational andRadical Equations 266

Quadratic Functions

The percentage of tufted puffin eggs that hatch during a breeding season de-

pends very much on the sea surface temperature of the surrounding area. A

slight increase or decrease from the optimal temperature results in a decrease

in the number of eggs hatched. This phenomenon can be modeled by a quad-ratic function. See Exercises 77 and 78 in Section 3.1. This chapter explores how

quadratic functions and equations arise, how to solve them, and how they are used in

various applications.

O b j e c t i v e s� Define the inverse of a

function

� Verify that two functions areinverses of each other

� Define a one-to-one function

� Define the conditions forthe existence of an inversefunction

� Find the inverse of a function

5.1 Inverse Functions

Inverse FunctionsSection 2.2 treated the composition of functions, which entails using the output of

one function as the input for another. Using this idea, we can sometimes find a function

that will undo the action of another function—a function that will use the output of

the original function as input, and will in turn output the number that was input to the

original function. A function that undoes the action of a function is called the inverseof .

As a concrete example of undoing the action of a function, Example 1 presents a

function that converts a quantity of fuel in gallons to an equivalent quantity of that

same fuel in liters.

ff

T E X T B O O K F E A T U R E S�

xx

309050_fm_frontmatter.qxd 1/15/08 1:50 PM Page xx

xxi

ExamplesWell-marked and with descriptive titles, the text Examples further illustrate the subject matter beingdiscussed. In cases where the solution to an example may involvemultiple steps, the steps are presented in tabular format for better organization.

Example 1 Modeling Bacterial Growth

Example 1 in Section 5.3 builds upon this example. l

Suppose a bacterium splits into two bacteria every hour.

(a) Fill in Table 5.2.1, which shows the number of bacteria present, after hours.tP(t),

Table 5.2.2

(hours)

(number of bacteria)P(t)

t

Table 5.2.1

(hours)

(number of bacteria)P(t)

t 0 1 2 3 4 5 6 7 8

(b) Find an expression for

�Solution

(a) Since we start with one bacterium and each bacterium splits into two bacteria

every hour, the population is doubled every hour. This gives us Table 5.2.2.

P(t).

0 1 2 3 4 5 6 7 8

1 2 4 8 16 32 64 128 256

(b) To find an expression for note that the number of bacteria present after

hours will be double the number of bacteria present an hour earlier. This gives

Following this pattern, we find that Here, the independent variable, is in the exponent. This is quite different from the functions we

examined in the previous chapters, where the independent variable was raised to a

fixed power. The function is an example of an exponential function.

Check It Out 1: In Example 1, evaluate and interpret your result. �P(9)�

P(t)

t,P(t) � 2t.

P(3) � 2(P(2)) � 2(22) � 23; P(4) � 2(P(3)) � 2(23) � 24; . . . .

P(1) � 2(1) � 21; P(2) � 2(P(1)) � 2(2) � 4 � 22;

tP(t),

Example 1 Bacterial Growth

k This example builds on Example 1 of Section 5.2.

A bacterium splits into two bacteria every hour. How many hours will it take for the

bacterial population to reach 128?

�Solution Note that in this example, we are given the ending population and must

figure out how long it takes to reach that population. Table 5.3.1 gives the population

for various values of the time , in hours. (See Example 1 from Section 5.2 for

details.)

t

Table 5.3.1

(hours)

(number of bacteria)P(t) � 2t

t 0 1 2 3 4 5 6 7 8

1 2 4 8 16 32 64 128 256

From the table, we see that the bacterial population reaches 128 after 7 hours.

Put another way, we are asked to find the exponent such that .The answer is

.

Check It Out 1: Use the table in Example 1 to determine when the bacterial popu-

lation will reach 64. �

�

t � 7

2t � 128t

�

Linked ExamplesWhere appropriate, some examples are linkedthroughout a section or chapter to promote in-depth understanding and to build stronger connections between concepts. While each example can be taught on its own, it’s suggested that the student review examples from previous sections when they have a bearing on the problem under discussion.

Linked Examples are clearly marked with an icon. l

�

STEPS EXAMPLE

1. The inequality should be written so that one side

consists only of zero.�x2 � 5x � 4 � 0

2. Factor the expression on the nonzero side of the in-

equality; this will transform it into a product of two

linear factors.

(�x � 4)(x � 1) � 0

3. Find the zeros of the expression on the nonzero side

of the inequality—that is, the zeros of

These are the only values of at which the expression

on the nonzero side can change sign.To find the

zeros, set each of the factors found in the previous

step equal to zero, and solve for .

x � 1 � 0 ›fi x � 1

�x � 4 � 0 ›fi x � 4

x

x(�x � 4)(x �1).

4. If the zeros found in the previous step are distinct,

use them to break up the number line into three

disjoint intervals. Otherwise, break it up into just

two disjoint intervals. Indicate these intervals on

the number line.

−1 4320 1 5 6 x

�Solution

Example 2 Algebraic Solution of a Quadratic Inequality

Solve the inequality algebraically.�x2 � 5x � 4 � 0

xxi

309050_fm_frontmatter.qxd 1/15/08 1:51 PM Page xxi

xxii

Check It Out 3: Use the model in Example 3 to project the national debt in the year2012. �

�

� Check It OutFollowing every example, these exercises provide the student with anopportunity to try a problem similar to that presented in the example.

The answers to each Check It Out are provided in an appendix at theback of the book so that students will receive immediate feedback.

� Just in TimeJust in Time references, found in the margin of the text, are helpful inthat they reduce the amount of time needed to review prerequisite skills.They refer to content previously introduced for “on-the-spot” review.

xxii

WHAT REVIEWERS SAY ABOUT

JUST IN TIME

Some of the constants that appear in the definition of a polynomial function have spe-

cific names associated with them:

� The nonnegative integer n is called the degree of the polynomial. Polynomials are

usually written in descending order, with the exponents decreasing from left to

right.

� The constants . . . , are called coefficients.

� The term is called the leading term, and the coefficient is called the lead-ing coefficient.

� A function of the form is called a constant polynomial or a constantfunction.

f(x) � a0

ananxn

ana0, a1,

Just In TimeReview polynomials in Section P.4.

“I struggle every semester: Do I spend a week doing the re-view chapter? With the Just in Time feature I don’t have to; it gives me more time to teach!”

Dean Barchers, Red Rocks Community College

309050_fm_frontmatter.qxd 1/15/08 1:51 PM Page xxii

xxiii

� ObservationsObservations are integrated throughout various sections. They often follow graphs and help to highlightand analyze important features of the graphs shown.

Presented as bulleted lists, they help students focus onwhat is most important when they look at similar graphs.By studying Observations, students can learn to better in-terpret and analyze what they see.

Discover and Learn

In Example 3b, verify that the orderof the vertical and horizontal trans-lations does not matter by firstshifting the graph of down by 2 units and then shiftingthe resulting graph horizontally tothe left by 3 units.

f ( x) � � x�

Observations:

� The -intercept is

� The domain of is the set of all real numbers.

� From the sketch of the graph, we see that the range of is the set of all neganumbers, or in interval notation.

� As

� As Thus, the horizontal asymptote is the line y � 0.xl ��, h(x)l 0.

xl ��, h(x)l ��.

(��, 0)

h

h

(0,�1).y

Discover and LearnThese instructor-guided exercises are placed closest to the discussion of the topic to which they apply and encourage further exploration of the concepts at hand.

They facilitate student interaction and participation and can be used by the instructor for in-class discussions or group exercises.

�

Figure 5.2.6

y

−30

−25

−20

−15

−10

−5

5

−4 −3 −2 −1 4321 x

h(x) = −4x

xxiii

WHAT REVIEWERS SAY ABOUT

OBSERVATIONS ANDDISCOVER AND LEARN

“…[What Observations] helps us help students do is toanalyze what’s happening in a particular problem…it helpsyou pick it apart in a way that can be challenging some-times…to pick out and observe some of those details andsome of those characteristics that you want to come out…ithelps you enter into that conversation with the students.

“The Discover and Learn…some of those kinds of prob-lems push you to go beyond a service understanding of what itis you’re talking about.”

Stephanie Sibley, Roxbury Community College

309050_fm_frontmatter.qxd 1/15/08 1:51 PM Page xxiii

xxiv

Technology Notes Technology Notes appear in the marginsto support the optional use of graphing calculator technology. Look for the

graphing calculator icon .

Sometimes the Notes acknowledge the limitations of graphing calculator technol-ogy, and they often provide tips on ways towork through those limitations.

�

Technology Note

Use a table of values to finda suitable window to graph

One possible window size is [0, 30](5) by [0, 11000](1000). See Figure 4.2.9.

Keystroke Appendix:

Sections 6 and 7

Y1(x) � 10000(0.92)x.

Figure 4.2.9

X Y1

X=0

051015202530

100006590.84343.928631886.91243.6819.66

300

11,000

0

xxiv

WHAT REVIEWERS SAY ABOUT

TECHNOLOGY NOTES

“I like the fact that it says what you can do with the technology asopposed to try to tell you the step-by-step process of how to do it.”

Aaron Levin, Holyoke Community College

“I like the way it refers you to the keystrokes.”

Brian Hons, San Antonio College-San Antonio

Example 3 Graphing a System of Inequalities

Graph the following system of inequalities.

�Solution To satisfy this system of inequalities, we must shade the area aboveand below

1. In the Y= Editor, enter in Y1 and then use the key to move to the leftmost end of the screen. Press to activate the “shade above” com-mand. See Figure A.8.7.

2. In the Y= Editor, enter in Y2 and then use the key to move to the leftmost end of the screen. Press to activate the “shade below”command. See Figure A.8.7.

ENTERENTERENTER

�

X, T, u, n(�)

ENTERENTER

�

X, T, u, n

y � �x.y � x

�y � xy � �x

� Keystroke Appendix A Keystroke Guide at the end of the book orientsstudents to specific keystrokes for the TI-83/84 series of calculators.

309050_fm_frontmatter.qxd 1/15/08 1:52 PM Page xxiv

xxvxxv

6.2 Key Points

� Definitions of trigonometric functions for right triangles

Sine: Cosecant:

Cosine: Secant:

Tangent: Cotangent:

� The following cofunction identities hold for all acute angles

� Sine and cosine of 30º, 45º, 60º:

sine 45� � cos 45� ��22

; sin 30� � cos 60� �12

; cos 30� � sin 60� ��32

csc(90� � �) � sec �sec(90� � �) � csc �

cot(90� � �) � tan �tan(90� � �) � cot �

cos(90� � �) � sin �sin(90� � �) � cos �

�.

cot � �adjopp

tan � �oppadj

sec � �hypadj

cos � �adjhyp

csc � �hypopp

sin � �opphyp

qAdjacent

OppositeHypotenuse

� Notes to the Student Placed within the exposition where appropriate, these Notesspeak to the reader in a conversational, one-on-one tone.Notes may be cautionary or informative, providing tips onavoiding common errors or further information on the topic at hand.

Key Points �

Key Points are presented in bulleted format at theend of each section. These easy-to-read summaries review the topics that have just beencovered.

Note You cannot verify an identity by substituting just a few numbers and

noting that the equation holds for those numbers. The identity must be verified

for all values of x in the domain of definition, and this has to be done

algebraically.

Note The symbol for infinity, is not a number. Therefore, it cannot be

followed by the bracket symbol in interval notation. Any interval extending

infinitely is denoted by the infinity symbol followed by a parenthesis. Similarly,

the symbol is preceded by a parenthesis.��

�,

WHAT REVIEWERS SAY ABOUT

THE KEYSTROKE GUIDE

“This [technology] appendix will help the TAs learn how to use the calculator (since they are good book learners), thenthey can help their students…So this helps immensely fromthe faculty coordinator’s point of view.”

David Gross, University of Connecticut

309050_fm_frontmatter.qxd 1/15/08 1:52 PM Page xxv

xxvi

Section-Ending ExercisesThe section-ending exercises are organized as follows: Just In Time Exercises(where appropriate), Skills, Applications, and Concepts. Exercises that encourageuse of a graphing calculator are denoted with an icon.

�Skills This set of exercises will reinforce the skills illus-

trated in this section.

In Exercises 5–34, solve the exponential equation. Round to threedecimal places, when needed.

5. 6.

7. 8.

9. 10.

11. 12.

13. 14. 3x � 72x � 5

5ex � 604ex � 36

6x �1

2164x �

1

16

10x � 0.000110x � 1000

72x � 495x � 125

6.7 Exercises

�Just in Time Exercises These exercises correspond to the

Just in Time references in this section. Complete them to

review topics relevant to the remaining exercises.

For Exercises 1–4, use the definition of f(x) as given by the followingtable.

1. Find . 2. Find .

3. Find . 4. Find .( f �1 � f )(4)( f � f �1)(4)

f �1(�1)f �1(�2)

x f(x)

5

3

1

4 �1

�2

�1

�2

Skills �

These exercises reinforce the skills illustrated in thesection.

Just in TimeExercisesThese exercises correspondto the Just in Time references that appear inthe section. By completingthese exercises, studentsreview topics relevant tothe Skills, Applications,and Concepts exercisesthat follow.

�

309050_fm_frontmatter.qxd 1/15/08 1:52 PM Page xxvi

xxviixxvii

55. Environment Sulfur dioxide (SO2) is emitted bypower-generating plants and is one of the primarysources of acid rain. The following table gives the totalannual SO2 emissions from the 263 highest-emittingsources for selected years. (Source: Environmental Pro-tection Agency)

(a) Let t denote the number of years since 1980. Makea scatter plot of sulfur dioxide emissions versus t.

(b) Find an expression for the cubic curve of best fit forthis data.

(c) Plot the cubic model for the years 1980–2005.Remember that for the years 2001–2005, the curvegives only a projection.

(d)Forecast the amount of SO2 emissions for the year2005 using the cubic function from part (b).

(e) Do you think the projection found in part (d) isattainable? Why or why not?

(f ) The Clean Air Act was passed in 1990, in part toimplement measures to reduce the amount of sulfurdioxide emissions. According to the model presentedhere, have these measures been successful? Explain.

Annual SO2 EmissionsYear (millions of tons)

1980 9.4

1985 9.3

1990 8.7

1994 7.4

1996 4.8

1998 4.7

2000 4

�Concepts This set of exercises will draw on the ideas pre-sented in this section and your general math background.

90. Do the equations and have the same solutions? Explain.

91. Explain why the equation has no solution.

92. What is wrong with the following step?

93. What is wrong with the following step?

In Exercises 94–97, solve using any method, and eliminate extra-neous solutions.

94. 95.

96. 97. ln �2x � 3� � 1log5 �x � 2� � 2

elog x � eln(log x) � 1

2x�5 � 34x fi x � 5 � 4x

log x � log(x � 1) � 0 fi x(x � 1) � 0

2ex � �1

2 ln x � 1ln x2 � 1

“The quality of exercises is outstanding. I found myself applauding the author for her varied applications problems—they are excellent and representative of the subject matter.”

Kevin Fox, Shasta College

“The one feature that I most appreciate is the ‘Concepts’problems incorporated in the homework problems of most sections.I feel that these problems provide a great opportunity to encouragestudents to think and to challenge their understanding.”

Bethany Seto, Horry-Georgetown Technical College

WHAT REVIEWERSSAY ABOUT

THE EXERCISES

� ApplicationsA wide range of Applications are provided, emphasizing how the math is applied in thereal world.

� ConceptsThese exercises appear toward the end of thesection-ending exercise sets. They are designedto help students think critically about the content in the existing section.

309050_fm_frontmatter.qxd 1/15/08 1:53 PM Page xxvii

xxviii

� Chapter SummaryThis unique, three-column format, broken downby section, provides the ultimate study guide.

Definition of an inverse functionLet f be a function. A function is said tobe the inverse function of f if the domainof is equal to the range of f and, for every

in the domain of f and every in thedomain of

The notation for the inverse function of f isf �1.

g( y) � x if and only if f (x) � y.

g,yx

g

g

Chapter 5 SummarySection 5.1 Inverse FunctionsConcept Illustration Study and Review

Graph of a function and its inverseThe graphs of a function and its inversefunction are symmetric with respect tothe line y � x.

f �1f

The graphs of and

are pictured. Note the

symmetry about the line y � x.

f �1(x) �x � 1

4

f (x) � 4x � 1 Examples 5, 6

Chapter 5 Review,Exercises 13–16

Continued

One-to-one functionA function is one-to-one if implies For a function to have aninverse, it must be one-to-one.

a � b.f (a) � f (b)f

The function is one-to-one,whereas the function is not.g(x) � x2

f (x) � x3 Example 4

Chapter 5 Review,Exercises 5–12

Composition of a function and its inverseIf is a function with an inverse function

then• for every in the domain of is

defined and .• for every in the domain of

is defined and .f ( f �1(x)) � xf ( f �1(x))f �1,x

f �1( f (x)) � xf �1( f (x))f,x

f �1,f

Let and Note

that Similarly,

.f( f �1(x)) � 4�x � 14 � � 1 � x

f �1( f (x)) �(4x � 1) � 1

4� x.

f �1(x) �x � 1

4.f (x) � 4x � 1 Examples 2, 3

Chapter 5 Review,Exercises 1–4

The inverse of is

f �1(x) �x � 1

4.

f (x) � 4x � 1 Examples 1, 2

Chapter 5 Review,Exercises 1–12

y = xf (x) = 4x + 1

f −1(x) = x − 14

y

−4

−4 −3

−2

−2 −1−1

123

4321 x

4

The first column,“Concept,” describesthe mathematicaltopic in words.

The second column,“Illustration,” showsthis concept beingperformed mathematically.

The third column,“Study and Review,”provides suggestedexamples and chapter review exercises that shouldbe completed to re-view each concept.

WHAT REVIEWERS SAY ABOUT

THE CHAPTER SUMMARY

“I like the tabular, column forms. It helps the students or-ganize what they’re looking at.”

Wayne Lee, St. Philips College

“I like how they give examples referring back. If you struggle a little bit with ‘this,’ look at ‘these’ particular prob-lems.You don’t have to go through and try to pick somethingout. It tells you right there what to go back and look at.”

Don Williamson Jr., Chadron State College

309050_fm_frontmatter.qxd 1/15/08 1:53 PM Page xxviii

xxixxxix

� Chapter Review Exercises Each chapter concludes with an extensive exercise set, broken down by section, so that students can easily identifywhich sections of the chapter they have mastered and whichsections might require more attention.

Chapter 5 Review ExercisesSection 5.1In Exercises 1–4,verify that the functions are inverses of each other.

1.

2.

3.

4.

In Exercises 5–12, find the inverse of each one-to-one function.

5. 6.

7.

8.

9.

10.

11.

12.

In Exercises 13–16, find the inverse of each one-to-one function.Graph the function and its inverse on the same set of axes, makingsure the scales on both axes are the same.

13. 14.

15. 16. f(x) � x2 � 3, x � 0f (x) � �x3 � 1

f (x) � 2x � 1f (x) � �x � 7

g(x) � 3x2 � 5, x � 0

g(x) � �x2 � 8, x � 0

f(x) � �2x3 � 4

f(x) � x3 � 8

f(x) � �2x �53

f(x) � �3x � 6

g(x) �23

xf(x) � �45

x

f(x) � �x2 � 1, x � 0; g(x) � �1 � x

f(x) � 8x3; g(x) ��3 x2

f(x) � �x � 3; g(x) � �x � 3

f(x) � 2x � 7; g(x) �x � 7

2

Section 5.325. Complete the table by filling in the exponential statements

that are equivalent to the given logarithmic statements.

26. Complete the table by filling in the logarithmic statementsthat are equivalent to the given exponential statements.

In Exercises 27–36, evaluate each expression without using acalculator.

27. 28.

29. 30.

31. 32.

33. 34. ln e�1ln �3 e

ln e1�2log �10

log717

log9 81

log6136

log5 625

Logarithmic ExponentialStatement Statement

log5125

� �2

log 0.1 � �1

log3 9 � 2

Exponential LogarithmicStatement Statement

8�1 �18

41�5 � �5 4

35 � 243

Chapter 5 Test1. Verify that the functions and

are inverses of each other.

2. Find the inverse of the one-to-one function

3. Find given Graph f and on the same set of axes.

In Exercises 4–6, sketch a graph of the function and describe itsbehavior as .

4.

5.

6.

7. Write in exponential form:

8. Write in logarithmic form:

In Exercises 9 and 10, evaluate the expression without using acalculator.

9. 10.

11. Use a calculator to evaluate to four decimalplaces.

12. Sketch the graph of Find all asymp-totes and intercepts.

In Exercises 13 and 14, write the expression as a sum or differenceof logarithmic expressions. Eliminate exponents and radicals whenpossible.

13. 14. ln(e2x2y)log �3 x2y4

f(x) � ln(x � 2).

log7 4.91

ln e3.2log8164

25 � 32.

log61

216� �3.

f(x) � e�2x

f(x) � 2�x � 3

f(x) � �3x � 1

xl ��

f �1x � 0.f(x) � x2 � 2,f �1(x)

f(x) � 4x3 � 1.

g(x) �x � 1

3f(x) � 3x � 1 In Exercises 17–22, solve.

17. 18.

19. 20.

21.

22.

23. For an initial deposit of $3000, find the total amount in abank account after 6 years if the interest rate is 5%, com-pounded quarterly.

24. Find the value in 3 years of an initial investment of $4000at an interest rate of 7%, compounded continuously.

25. The depreciation rate of a laptop computer is about 40%per year. If a new laptop computer was purchased for$900, find a function that gives its value t years after pur-chase.

26. The magnitude of an earthquake is measured on the

Richter scale using the formula , where I

represents the actual intensity of the earthquake and isa baseline intensity used for comparison. If an earth-quake registers 6.2 on the Richter scale, express its in-tensity in terms of .

27. The number of college students infected with a coldvirus in a dormitory can be modeled by the logistic

function where t is the number of days

after the breakout of the infection.(a) How many students were initially infected?(b) Approximately how many students will be infected

after 10 days?

N(t) �120

1 � 3e�0.4t ,

I0

I0

R(I) � log� II0

�

log x � log(x � 3) � 1

ln(4x � 1) � 0

200e0.2t � 8004ex�2 � 6 � 10

4x � 7.162x � 363x�1

Chapter Test �

Each chapter ends with a test thatincludes questions based on eachsection of the chapter.

309050_fm_frontmatter.qxd 1/15/08 1:53 PM Page xxix

309050_fm_frontmatter.qxd 1/15/08 1:53 PM Page xxx

College Algebra andTrigonometry:

Building Concepts and Connections

instructor’s annotated edition

309050_fm_frontmatter.qxd 1/15/08 1:53 PM Page xxxi

309050_fm_frontmatter.qxd 1/15/08 1:53 PM Page xxxii