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Functions Modeling Change A Preparation For Calculus Third Edition 3 Edition Eric Connally FUNCTIONS MODELING ac https://ebookbell.com/product/functions-modeling-change-a-preparation- for-calculus-third-edition-3-edition-eric-connally-2324044 Functions Modeling Change A Preparation For Calculus 4th Edition 4th Eric Connally https://ebookbell.com/product/functions-modeling-change-a-preparation- for-calculus-4th-edition-4th-eric-connally-2372872 Functions Modeling Change A Preparation For Calculus 3rd Edition Eric Connally FUNCTIONS MODELING CHANGE https://ebookbell.com/product/functions-modeling-change-a-preparation- for-calculus-3rd-edition-eric-connally-2382846 Functions And Change A Modeling Approach To College Algebra 6th Edition Bruce Crauder https://ebookbell.com/product/functions-and-change-a-modeling- approach-to-college-algebra-6th-edition-bruce-crauder-48814458 O: FUNCTIONS MODELING CHANGE: A Preparation for Calculus Fifth Edition Produced by the Calculus Consortium and initially funded by a National Science Foundation Grant. Eric Connally Deborah Hughes-Hallett Harvard University Extension The University of Arizona Andrew M. Gleason Philip Cheifetz Harvard University Nassau Community College Ann Davidian Daniel E. Flath Gen. Douglas MacArthur HS Macalester College Selin Kalayciog8lu Brigitte Lahme New York University Sonoma State University Patti Frazer Lock Guadalupe I. Lozano St. Lawrence University The University of Arizona William G. McCallum Jerry Morris The University of Arizona Sonoma State University Karen Rhea Ellen Schmierer University of Michigan Nassau Community College Pat Shure Adam H. Spiegler University of Michigan Loyola University Chicago Carl Swenson Aaron D. Wootton Seattle University University of Portland Elliot J. Marks with the assistance of Frank Avenoso Douglas Quinney Katherine Yoshiwara Nassau Community College University of Keele Los Angeles Pierce College WILEY Dedicated to Ben, Jonah, and Isabel PUBLISHER Laurie Rosatone ACQUISITIONS EDITOR Joanna Dingle ASSOCIATE EDITOR Jacqueline Sinacori MARKETING MANAGER Kimberly Kanakes SENIOR PRODUCT DESIGNER Tom Kulesa SENIOR CONTENT MANAGER Karoline Luciano SENIOR PRODUCTION EDITOR Ken Santor FREELANCE PROJECT EDITOR Anne Scanlan-Rohrer EDITORIAL PROGRAM ASSISTANT Courtney Welsh MARKETING ASSISTANT Jesse Adler COVER DESIGNER Madelyn Lesure COVER AND CHAPTER OPENING PHOTO OPatrick Zephyr/Patrick Zephyr Nature Photography This book was set in Stix by the Consortium using TeX, Mathematica, and the package AsTeX, which was written by Alex Kasman. The process was managed by Elliot Marks. Copyright 02015, 2012, 2011, 2006, 2003 John Wiley 8 Sons, Inc. All rights reserved. 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ISBN-13 978-1-118-58319-7 (Paper) ISBN-13 978-1-118-98630-1 (Cloth) ISBN-13 978-1-118-94258-1 (BRV) vi Preface We provide students and instructors quick means of assessing comprehension before moving on by using the true-false Strengthen Your Understanding problems at the end of each chapter. Our central theme, functions as models of change, links the components of our precalculus curriculum. Algebra is integrated where appropriate. Topics are fewer in number than it is customary so they can be treated in greater depth. The topics are those essential to the study of calculus. Problems involving real data give students practice with modeling. We include both classic and current applications to prepare students to model with mathematics in a variety of contexts. Our problems allow students to become proficient in the use of technology, including symbolic manipu- lators, computers, tablets, and online software, as appropriate. Our precalculus materials allow for a broad range of teaching styles. They are flexible enough for use in large lecture halls, small classes, or in group or lab settings. Changes in the Fifth Edition The fifth edition reflects the many helpful suggestions from users while preserving the focus and guiding principles of previous editions. We have made the following changes: e Many examples and problems are new or have been rewritten. Data has been updated and new data introduced. e The three chapters on trigonometry have been reorganized and rewritten: — Trigonometric functions on the circle are introduced both in radians and degrees in Chapter 7, highlighting the natural relationship between radians and the unit circle as soon as periodic functions are introduced. — Sinusoidal functions modeling periodic phenomena and simple trigonometric equations are also introduced in Chapter 7, while more involved trigonometric models and equations requiring relation- ships such as double-angle identities are treated in Chapter 9. — Phase shift has been made an optional topic in Chapter 7. — Triangle trigonometry is discussed separately in Chapter 8, after trigonometric and sinusoidal func- tions are treated in Chapter 7. A briefexploration of linear inequalities has been integrated with the material on solving linear equations in Chapter 1. Vertical and horizontal shifts are introduced in Chapter 2, and referenced in Chapter 3 when introducing the vertex form of a quadratic equation. Shifts are reviewed at the beginning of Chapter 6 and considered in combination with other transformations. Odd and even functions are introduced by looking at invariance of certain functions under reflections, and thus better integrated with the transformation focus of Chapter 6. The effect of changing the order of transformations, the last section in Chapter 6 in the fourth edition, has been shortened and included in the previous section. The section on power functions in Chapter 11 has been rewritten to increase the focus on graphical behavior and proportionality. Examples on average rate of change have been added throughout the book, such as for exponential functions (in Chapter 5) and periodic functions (in Chapters 7 and 9). WileyPLUS, the primary online resource suite paired with the textbook, has been updated with improved problems and hints, including many new problems from the fifth edition. Preface vii What Student Background is Expected? Students using this book should have successfully completed a course in intermediate algebra or high school algebra II. The book is thought-provoking for well-prepared students while still accessible to students with weaker backgrounds. Providing numerical, graphical, and algebraic approaches builds on different student strengths and provides students with a variety of ways to master the material. Multiple representations give students tools to persist, lowering failure rates. Our Experiences The first four editions of this book were used at hundreds of schools around the country in a wide variety of settings. It has been used successfully in both semester and quarter systems, in large lectures and small classes as well as in full-year courses in secondary schools. It has also been used in computer labs and small groups, often with the integration of a number of different technologies. Content The central theme of this book is functions as models of change. We emphasize that functions can be grouped into families and that functions can be used as models. We explore how function characteristics connect to difference quotients and rates of change, naturally previewing key calculus ideas. Because linear, quadratic, exponential, power, and periodic functions are most frequently used to model physical phenomena, they are introduced before polynomial and rational functions. Once introduced, a family of functions is compared and contrasted with other families of functions. A large number of the examples that students see in this precalculus course are real-world problems. By the end of the course, we hope that students will use functions to help them understand the world in which they live. We include non-routine problems to emphasize that such problems are not only part of mathematics, but in some sense are the reason for doing mathematics. Technology The book does not require any specific software or technology. Instructors have used the material with graph- ing calculators, graphing software, or scientific calculators. Chapter 1: Linear Functions and Change This chapter introduces the concept of a function as well as graphical, tabular, symbolic, and verbal represen- tations of functions, discussing the advantages and disadvantages of each representation. It introduces rates of change and uses them to characterize linear functions. Examples on modeling with linear functions, including interpreting linear inequalities, are discussed. A section on fitting a linear function to data is included. The Skills Refresher section for Chapter 1 reviews linear equations, linear inequalities, and the coordi- nate plane. Chapter 2: Functions This chapter studies functions in more detail. It introduces domain, range, previews function shifts and the concepts of composite and inverse functions, and investigates the idea of concavity using rates of change. A section on piecewise functions is included. Chapter 3: Quadratic Functions This chapter introduces the standard, factored, and vertex forms of a quadratic function and explores their relationship to graphs, including shifts. The family of quadratic functions provides an opportunity to see the effect of parameters on functional behavior. The Skills Refresher section for Chapter 3 reviews factoring, completing the square, and quadratic equa- tions. Preface ix Chapter 13: Sequences and Series This chapter introduces arithmetic and geometric sequences and series and their applications. Chapter 14: Parametric Equations and Conic Sections The concluding chapter looks at parametric equations, implicit functions, hyperbolic functions, and conic sections: circles, ellipses, and hyperbolas. The chapter includes a section on the geometrical properties of the conic sections and their applications to orbits. Note: Chapter 14 is available online only. Supplementary Materials The following supplementary materials are available for the fifth edition: e The Instructor?s Manual contains teaching tips, lesson plans, syllabi, and worksheets. It has been expanded and revised to include worksheets, identification of technology-oriented problems, and new syllabi. (ISBN 978-1-119-01383-9) e The Printed Test Bank contains test questions arranged by section. e The Instructor”s Solution Manual has complete solutions to all problems. (ISBN 978-1-118-94162-1) e The Student Solution Manual has complete solutions to half of the odd-numbered problems. (ISBN 978-1-118-94163-8) e The Computerized Test Bank, available in both PC and Macintosh formats, allows instructors to create, customize, and print a test containing any combinations of questions from a large bank of questions. Instructors can also customize the questions or create their own. e Classroom Activities are posted at the book companion website. These activities were developed to facilitate in-class group work as well as to introduce new concepts and to practice skills. In addition to the blank copies for each activity that can be handed out to the students, a copy of the activity with fully worked out solutions is also available. e The Book Companion Site at www.wiley.com/college/connally contains all instructor supplements. e WileyPLUS is a powerful online suite of teaching and learning resources tightly integrated with the text. WileyPLUS enables instructors to assign, deliver and grade individually customized homework assign- ments using exercises and problems from the text. Students receive immediate feedback on their home- work and access to full solutions to assigned problems electronically. Students may also access hints to the problems. In addition to online homework, WileyPLUS provides student tutorials, an instructor grade- book, integrated links to the electronic version of the text, and all of the text's supplemental materials. For more information, visit www. wiley.com/college/wileyplus or contact your local Wiley representative for more details. e Mini-lecture Videos linked with examples in the WileyPLUS student version of the text provide greater detail to the solution of examples in each section of the text. These may assist students in reading the text prior to class or in reviewing material after class. e The Faculty Network is a peer-to-peer network of academic faculty dedicated to the effective use of technology in the classroom. This group can help you apply innovative classroom techniques, implement specific software packages, and tailor the technology experience to the specific needs of each individual class. Visit www.wherefacultyconnect.com or ask your Wiley representative for details. ConcepTests ConcepTests, modeled on the pioneering work of Harvard physicist Eric Mazur, are questions designed to promote active learning during class, particularly (but not exclusively) in large lectures. Our evaluation data show students taught with ConcepTests outperformed students taught by traditional lecture methods 73% ver- sus 17% on conceptual questions, and 63% versus 54% on computational problems. ConcepTests arranged by x Preface section are available in PowerPoint and Classroom Response System-ready formats from your Wiley repre- sentative. (ISBN 978-1-118-94161-4) Acknowledgments We would like to thank the many people who made this book possible. First, we would like to thank the National Science Foundation for their trust and their support; we are particularly grateful to Jim Lightbourne and Spud Bradley. We are also grateful to our Advisory Board for their guidance: Benita Albert, Lida Barrett, Simon Bernau, Robert Davis, Lovenia Deconge-Watson, John Dossey, Ronald Douglas, Eli Fromm, Bill Haver, Don Lewis, Seymour Parter, John Prados, and Stephen Rodi. Working with Laurie Rosatone, Anne Scanlan-Rohrer, Ken Santor, Shannon Corliss, Joanna Dingle, Kimberly Kanakes, Jacqueline Sinacori, Courtney Walsh, and Madelyn Lesure at John Wiley is a pleasure. We appreciate their patience and imagination. Many people have contributed significantly to this text. They include: Lauren Akers, Fahd Alshammari, David Arias, Tim Bean, Charlotte Bonner, Bill Bossert, Brian Bradie, Noah S. Brannen, Mike Brilleslyper, Donna Brouillette, Matthew M. Campbell, Jo Cannon, Ray Cannon, Kenny Ching, Anna Chung, Pierre Cres- sant, Marcia Crump, Laurie Delitsky, Bob Dobrow, Helen M. Doerr, lan Dowker, Carolyn Edmond, Maryann Faller, Aidan Flanagan, Brendan Fry, Brad Garner, Carrie Garner, John Gerke, Christie Gilliland, Wynne Guy, Donnie Hallstone, David Halstead, Larry Henly, Dean Hickerson, Jo Ellen Hillyer, Bob Hoburg, Phil Hotchkiss, Mike Huffman, Mac Hyman, Rajini Jesudason, Loren Johnson, David Jones, Scott Kaplowitch, Nazanin Karimi, Thomas Kershaw, Mary Kilbride, Steve Kinholt, Kandace Kling, Angela Kubena, Rob LaQuaglia, Barbara Leasher, Kenneth Lemp, Richard Little, David Lovelock, Guadalupe Lozano Terán, Nicholas Lyktey, Chaimaa Makoudi, Len Malinowski, Nancy Marcus, Kate McGivney, Gowri Meda, Bob Megginson, Deborah Moore, Eric Motylinski, Bill Mueller, Michael Nakamaye, Kyle Niedzwiecki, Karina Nielsen, Kathryn Oswald, Igor Padure, Bridget Neale Paris, Janet Ray, Ritam Ray, Ken Richardson, Halip Saifi, Sharon Sanders, Mary Schumacher, Mike Seery, Mike Sherman, Donna Sherrill, Max Shuchman, Fred Shure, Kanwal Singh, Myra Snell, Regina Souza, Natasha Speer, Sonya Stanley, Michael Steuer, Jim Stone, Peggy Tibbs, Jeff Taft, Elias Toubassi, Jerry Uhl, Pat Wagener, Benjamin West, Dale Winter, Timothy Wise- carver, and Xianbao Xu. Reports from the following reviewers were most helpful in shaping the second, third, fourth, and fifth edi- tions: Victor Akatsa, Jeffrey Anderson, Beth Borel, Linda Braddy, Michael Brassington, Ingrid Brown-Scott, Linda Casper, Kim Chudnick, Ted Coe, Ray Collings, Joe Coyle, Pam Crawford, Marcia Crump, Monica Davis, Laurie Delitsky, Phyllis Desormeaux, Helen Doerr, Diane Downie, Peter Dragnev, Patricia Dueck, Julie Fisher, Jennifer Fowler, Alyne Fulte, David Gillette, Jack Green, Zdenka Guadarrama, Donnie Hall- stone, Jeff Hoherz, Majid Hosseini, Rick Hough, Ann Humes, Bryan Ingham, Mary Lou Jumonville, Pallavi Ketkar, William Kiele, Mile Krajcevski, John LaMaster, Richard Lane, Debbie Lee, Phyllis Leonard, Daphne MacLean, Diane Mathios, Krista Maxson, Michael McAfee, Vince McGarry, Maria Miles, Laura Moore- Mueller, Ellen Musen, Dave Nolan, Linda O” Brien, Chris Parks, Scott Perry, Jeffrey S. Powell, Anne Praderas, Michael Price, Mary Rack, Gregory Rhoads, Joe Rody, Emily Roth, John Sawka, Amy N. Schachle, Barbara Shabell Deirdre Smith, Ernie Solheid, Regina P. Souza, Sandy Spears, Diana Staats, Jonathan Stadler, Mary Jane Sterling, Dennis Stramiello, Debbie Strance, Allison Sutton, John Thomason, Diane Van Nostrand, Jim Vicich, Linda Wagner, Nicole Williams, Jim Winston, Vauhn Wittman-Grahler, Bruce Yoshiwara, Fang Zhao, and Xinyun Zhu. Special thanks are owed to Faye Riddle for administering the project and to Alex Kasman for his software support. Eric Connally Deborah Hughes-Hallett Andrew M. Gleason Philip Cheifetz Ann Davidian Dan Flath Selin Kalaycioglu Brigitte Lahme Patti Frazer Lock Guadalupe I. Lozano Elliot J. Marks William G. McCallum Jerry Morris Karen Rhea Ellen Schmierer Pat Shure Adam H. Spiegler Carl Swenson Aaron D. Wootton Table of Contents 1 LINEAR FUNCTIONS AND CHANGE 1.1 FUNCTIONS AND FUNCTION NOTATION 2 12 RATEOFCHANGE 10 1.3 LINEAR FUNCTIONS — 18 1.4 FORMULAS FOR LINEAR FUNCTIONS 27 1.5 MODELING WITH LINEAR FUNCTIONS 37 1.6 FITTING LINEAR FUNCTIONS TO DATA — 46 REVIEW PROBLEMS 52 STRENGTHEN YOUR UNDERSTANDING 60 SKILLS REFRESHER FOR CHAPTER ONE: LINEAR EQUATIONS — 62 2 FUNCTIONS 69 2.1 INPUT AND OUTPUT 70 2.2 DOMAIN AND RANGE 78 2.3 PIECEWISE-DEFINED FUNCTIONS 84 2.4 PREVIEW OF TRANSFORMATIONS: SHIFTS 90 2.5 PREVIEW OF COMPOSITE AND INVERSE FUNCTIONS 97 2.6 CONCAVITY 104 REVIEW PROBLEMS — 109 STRENGTHEN YOUR UNDERSTANDING 113 3 QUADRATIC FUNCTIONS 115 3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS 3.2 THE VERTEX OF A PARABOLA — 122 REVIEW PROBLEMS — 129 STRENGTHEN YOUR UNDERSTANDING — 130 SKILLS REFRESHER FOR CHAPTER 3 131 SKILLS FOR FACTORING — 131 COMPLETING THE SQUARE — 136 xii 116 Contents xiii 4 EXPONENTIAL FUNCTIONS 139 4.1 INTRODUCTION TO THE FAMILY OF EXPONENTIAL FUNCTIONS — 140 4.2 COMPARING EXPONENTIAL AND LINEAR FUNCTIONS — 149 4.3 GRAPHS OF EXPONENTIAL FUNCTIONS 157 4.4 APPLICATIONS TO COMPOUND INTEREST 165 45 THENUMBERe 168 REVIEW PROBLEMS 176 STRENGTHEN YOUR UNDERSTANDING — 182 SKILLS REFRESHER FOR CHAPTER 4: EXPONENTS 183 5 LOGARITHMIC FUNCTIONS 187 5.1 LTOGARITHMS AND THEIR PROPERTIES — 188 5.2 LOGARITHMS AND EXPONENTIAL MODELS 195 5.3 THE LOGARITHMIC FUNCTION AND ITS APPLICATIONS 203 5.4 LOGARITHMIC SCALES — 214 REVIEW PROBLEMS — 225 STRENGTHEN YOUR UNDERSTANDING 228 SKILLS REFRESHER FOR CHAPTER 5: LOGARITHMS — 229 6 TRANSFORMATIONS OF FUNCTIONS AND THEIR GRAPHS 233 6.1 SHIFTS, REFLECTIONS, AND SYMMETRY 234 6.2 VERTICAL STRETCHES AND COMPRESSIONS 243 6.3 HORIZONTAL STRETCHES AND COMBINATIONS OF TRANSFORMATIONS — 250 REVIEW PROBLEMS — 259 STRENGTHEN YOUR UNDERSTANDING 263 Contents xv 10 COMPOSITIONS, INVERSES, AND COMBINATIONS OF FUNCTIONS 397 10.1 COMPOSITION OF FUNCTIONS 398 10.2 INVERTIBILITY AND PROPERTIES OF INVERSE FUNCTIONS — 404 10.3 COMBINATIONS OF FUNCTIONS 414 REVIEW PROBLEMS — 424 STRENGTHEN YOUR UNDERSTANDING — 430 11 POLYNOMIAL AND RATIONAL FUNCTIONS 431 11.1 POWER FUNCTIONS AND PROPORTIONALITY — 432 11.2 POLYNOMIAL FUNCTIONS 443 11.3 THE SHORT-RUN BEHAVIOR OF POLYNOMIALS — 451 11.4 RATIONAL FUNCTIONS — 457 11.5 THE SHORT-RUN BEHAVIOR OF RATIONAL FUNCTIONS — 464 11.6 COMPARING POWER, EXPONENTIAL, AND LOG FUNCTIONS — 471 11.7 FITTING EXPONENTIALS AND POLYNOMIALS TO DATA 476 REVIEW PROBLEMS — 484 STRENGTHEN YOUR UNDERSTANDING 489 SKILLS REFRESHER FOR CHAPTER 11: ALGEBRAIC FRACTIONS — 491 12 VECTORS AND MATRICES 495 12.1 VECTORS 496 12.2 THE COMPONENTS OF A VECTOR — 503 12.3 APPLICATIONS OF VECTORS — 510 12.4 THE DOT PRODUCT 516 12.5 MATRICES 522 REVIEW PROBLEMS — 531 STRENGTHEN YOUR UNDERSTANDING 534 xvi Contents 13 SEQUENCES AND SERIES 535 13.1 SEQUENCES 536 13.2 DEFINING FUNCTIONS USING SUMS: ARITHMETIC SERIES 541 13.3 FINITE GEOMETRIC SERIES 548 13.4 INFINITE GEOMETRIC SERIES 553 REVIEW PROBLEMS 559 STRENGTHEN YOUR UNDERSTANDING — 561 14 PARAMETRIC EQUATIONS AND CONIC SECTIONS (Online Only) 14-1 14.1 PARAMETRIC EQUATIONS — 14-2 14.2 IMPLICITLY DEFINED CURVES AND CIRCLES — 14-11 14.3 ELLIPSES — 14-15 14.4 HYPERBOLAS — 14-18 14.5 GEOMETRIC PROPERTIES OF CONIC SECTIONS — 14-22 14.6 HYPERBOLIC FUNCTIONS — 14-36 REVIEW PROBLEMS — 14-40 STRENGTHEN YOUR UNDERSTANDING — 14-41 ANSWERS TO ODD PROBLEMS 563 INDEX 599 
