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PREFACE
xi
Our Mission
The goal of Precalculus: Building Concepts and Connections is to teach students to moreclearly see how mathematical concepts connect and relate. We set out to accomplishthis 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 Precalculus: Building Concepts and Connections,students will develop a better conceptual understanding of the subject and achievegreater 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.
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.
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.
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Right Triangle Approach versus Unit Circle Approach: A Closer LookIn 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.
In Chapter 6 of College Algebra and Trigonometry the author includes two sectionson right triangle trigonometry (Sections 6.2 and 6.3), that covers all angles, as well asa section on the unit circle (Section 6.4), that also 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
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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 ReinforceAppendix A Appendix A has been developed for students or instructors who want toreview prerequisite skills for the course.Topics include the real number system; expo-nents and scientific notation; roots, radicals, and rational exponents; polynomials; fac-toring; 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
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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/narasimhanP1e or contact yourlocal 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.
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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 Mizell
Austin 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
309060_fm_frontmatter.qxd 12/20/07 12:46 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
309060_fm_frontmatter.qxd 12/20/07 12:46 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
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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
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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
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� 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.
285
44.1 Inverse Functions 286
4.2 ExponentialFunctions 298
4.3 LogarithmicFunctions 313
4.4 Properties ofLogarithms 329
4.5 Exponential and LogarithmicEquations 337
4.6 Exponential,Logistic, and Logarithmic Models 347
Exponential and Logarithmic Functions
Population growth can be modeled in the initial stages by an exponential function,a type of function in which the independent variable appears in the exponent.A simple illustration of this type of model is given in Example 1 of Section 4.2,
as well as Exercises 30 and 31 of Section 4.6. This chapter will explore expo-
nential functions. These functions are useful for studying applications in a variety of
fields, including business, the life sciences, physics, and computer science. The expo-
nential functions are also invaluable in the study of more advanced mathematics.
C h a p t e r
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
4.1 Inverse Functions
Inverse FunctionsSection 2.1 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�
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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 Circular Motion
Example 1 in Section 5.6 builds upon this example. l
A child takes a ride on a merry-go-round at the playground. The horse she has
chosen is located 1 meter from the center of the merry-go-round. See Figure 5.1.1.
(a) What is the angle swept out as the child makes half a revolution about the axis of
the merry-go-round?
(b) What is the distance traversed by the child as he or she makes half a revolution on
the merry-go-round?
�Solution
(a) A full revolution is . Thus the angle swept out in making half a revolution is
.
(b) The distance D traversed by the child in making half a revolution about the axis of
the merry-go-round is given by half the circumference of a circle with a radius of
1 meter. The circumference of a circle is given by where r is the radius. Thus
meters.
Check It Out 1: In Example 1, what distance is traversed by the child as he or she
makes a quarter of a revolution about the center of the merry-go-round? �
The relationship between the angle swept out by a revolving object and the
distance traversed by that object is one we will explore in detail later in this section.
Angles and the xy Coordinate SystemAn angle is formed by rotating a ray (or half-line) about its endpoint.The initial sideof the angle is the starting position of the ray, and the terminal side of the angle is
the final position, the position of the ray after the rotation. The vertex of the angle is
the point about which the ray is rotated. Angles are usually denoted by lowercase
�
D �1
2(2�r) �
1
2(2�(1)) � �
2�r,
180�360�
Example 1 Using Values of Trigonometric Functions to Find Angles
k This example builds on Example1 in Section 5.1.
A child takes a ride on a carousel.The horse the child has chosen is located 1 meter
from the center of rotation of the carousel. Denote this starting point as (1, 0),
which is on the unit circle. Five seconds later, the child is at the point See Fig-
ure 5.6.1. At that time, what angle does the line from the center of the carousel to
the child and horse make with the line from the center of the carousel to their starting
point?
�Solution Because the child is traveling “on the unit circle,” his or her coordinates at
any given time are the values of the sine and the cosine of the angle swept out by the
carousel since it started to rotate. Thus and are the cosine and sine, respectively,
of the angle swept out in the first 5 seconds.To solve this problem, we work backwards—
that is, we must find an angle such that and See Figure 5.6.1.
Because and and lies in the first quadrant, we conclude
that
Check It Out 1: Suppose that 10 seconds after starting, the child from Example 1 is
at the point with coordinates At that time, what angle does the line from the �1
2,
�3
2 �.�
� ��
6.
��3
2,
1
2�sin� �1
2,cos� �
�3
2
sin � �1
2.cos � �
�3
2�
1
2
�3
2
�
��3
2,
1
2�.
�
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
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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.
Algebraic Methods for Verifying IdentitiesAnother useful strategy for verifying identities is to factor an expression in order tosimplify it.
Strategy 2 Factor
Apply a factoring technique, if possible, to a given expression.
Just in TimeReview factoring techniquesin Section A.5.
xxii
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JUST IN TIME
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� 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 4.2.6
y
−30
−25
−20
−15
−10
−5
5
−4 −3 −2 −1 4321 x
h(x) = −4x
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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.”
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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
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WHAT REVIEWERS SAY ABOUT
TECHNOLOGY NOTES
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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.
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5.2 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
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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
5.6 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.
�
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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.
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� 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 4 SummarySection 4.1 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 4 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 4 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 4 Review,Exercises 1–4
The inverse of is
f �1(x) �x � 1
4.
f (x) � 4x � 1 Examples 1, 2
Chapter 4 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
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� 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 4 Review ExercisesSection 4.1In 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 4.325. 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 4 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.
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Precalculus:Building Concepts and Connections
instructor’s annotated edition
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