Motivating Features to Help You Succeed! Your success in college algebra and trigonometry is important to us. To guide you to that success, we have created a textbook with features that promote learning and support various learning styles. These features are highlighted below. We encourage you to examine these features and use them to successfully complete this course. (cid:3) Prepare for This Section These exercises test your understanding of prerequisite skills and concepts that were covered earlier in the text. Mastery of these concepts is required for success in the following section. (cid:2) Motivating Applications Large selections of contemporary applications from many different disciplines demonstrate the utility of mathematics. (cid:3) Engaging Examples Examples are designed to capture your attention and help you master important concepts. (cid:3) Annotated Examples Step-by-step solutions are provided for each example. (cid:3) Try Exercises A reference to an exercise follows each worked example. This exercise provides you the opportunity to test your understanding by working an exercise similar to the worked example. (cid:3) Solutions to Try Exercises The complete solutions to the Try Exercises can be found in the Solutions to the Try Exercises appendix, starting page S1. (cid:2) Visualize the Solution When appropriate, both algebraic and graphical solutions are provided to help visualize the mathematics of the example and to create a link between the two. (cid:3) Mid-Chapter Quizzes These quizzes will help you assess your understanding of the concepts studied earlier in the chapter. They provide a mini-review of the chapter material. (cid:2) Chapter Test Prep This is a summary of the major concepts discussed in the chapter and will help you prepare for the chapter test. For each concept, there is a reference to a worked example illustrating how the concept is used and at least one exercise in the chapter review relating to that concept. This page intentionally left blank COLLEGE ALGEBRA AND TRIGONOMETRY This page intentionally left blank SEVENTH COLLEGE ALGEBRA EDITION AND TRIGONOMETRY mages Getty I Chad Ehlers/ Richard N. Aufmann Vernon C. Barker Richard D. Nation Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States College Algebra and Trigonometry, © 2011, 2008Brooks/Cole, Cengage Learning Seventh Edition ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may Richard N. Aufmann, Vernon C. Barker, be reproduced, transmitted, stored, or used in any form or by any means, graphic, Richard D. 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Content Project Manager: Jennifer Risden Library of Congress Control Number: 2009938510 Creative Director: Rob Hugel Art Director: Vernon Boes ISBN-13: 978-1-4390-4860-3 Print Buyer: Karen Hunt ISBN-10: 1-4390-4860-6 Rights Acquisitions Account Manager, Text: Roberta Broyer Brooks/Cole Rights Acquisitions Account Manager, 20Davis Drive Image: Don Schlotman Belmont, CA94002-3098 USA Production Service: Graphic World Inc. Text Designer: Diane Beasley Cengage Learning is a leading provider of customized learning solutions with office Photo Researcher: PrepressPMG locations around the globe, including Singapore, the United Kingdom, Australia, Copy Editor: Graphic World Inc. Mexico, Brazil, and Japan. Locate your local office at www.cengage.com/global. Illustrators: Network Graphics; Macmillan Publishing Solutions Cengage Learning products are represented in Canada by Nelson Cover Designer: Lisa Henry Education, Ltd. Cover Image: Chad Ehlers/Getty Images Compositor: MPS Limited, A Macmillan To learn more about Brooks/Cole, visit www.cengage.com/brookscole Company Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Printed in the United States of America 1 2 3 4 5 6 7 13 12 11 10 09 CONTENTS CHAPTER P Preliminary Concepts 1 P.1 The Real Number System 2 P.2 Integer and Rational Number Exponents 17 P.3 Polynomials 32 Mid-Chapter P Quiz 39 P.4 Factoring 40 P.5 Rational Expressions 49 P.6 Complex Numbers 59 Exploring Concepts with Technology 66 Chapter P Test Prep 67 Chapter P Review Exercises 70 Chapter P Test 73 CHAPTER 1 Equations and Inequalities 75 1.1 Linear and Absolute Value Equations 76 1.2 Formulas and Applications 83 1.3 Quadratic Equations 96 Mid-Chapter 1 Quiz 109 1.4 Other Types of Equations 110 1.5 Inequalities 123 1.6 Variation and Applications 136 Exploring Concepts with Technology 144 Chapter 1 Test Prep 145 Chapter 1 Review Exercises 148 Chapter 1 Test 151 Cumulative Review Exercises 152 CHAPTER 2 Functions and Graphs 153 2.1 Two-Dimensional Coordinate System and Graphs 154 2.2 Introduction to Functions 166 2.3 Linear Functions 186 Mid-Chapter 2 Quiz 200 2.4 Quadratic Functions 200 2.5 Properties of Graphs 213 2.6 Algebra of Functions 227 2.7 Modeling Data Using Regression 237 Exploring Concepts with Technology 248 Chapter 2 Test Prep 249 Chapter 2 Review Exercises 253 Chapter 2 Test 257 Cumulative Review Exercises 258 v vi CONTENTS CHAPTER 3 Polynomial and Rational Functions 259 3.1 Remainder Theorem and Factor Theorem 260 3.2 Polynomial Functions of Higher Degree 271 3.3 Zeros of Polynomial Functions 287 Mid-Chapter 3 Quiz 299 3.4 Fundamental Theorem of Algebra 299 3.5 Graphs of Rational Functions and Their Applications 307 Exploring Concepts with Technology 323 Chapter 3 Test Prep 324 Chapter 3 Review Exercises 328 Chapter 3 Test 331 Cumulative Review Exercises 332 CHAPTER 4 Exponential and Logarithmic Functions 333 4.1 Inverse Functions 334 4.2 Exponential Functions and Their Applications 346 4.3 Logarithmic Functions and Their Applications 358 4.4 Properties of Logarithms and Logarithmic Scales 369 Mid-Chapter 4 Quiz 380 4.5 Exponential and Logarithmic Equations 380 4.6 Exponential Growth and Decay 390 4.7 Modeling Data with Exponential and Logarithmic Functions 404 Exploring Concepts with Technology 416 Chapter 4 Test Prep 418 Chapter 4 Review Exercises 421 Chapter 4 Test 424 Cumulative Review Exercises 425 CHAPTER 5 Trigonometric Functions 427 5.1 Angles and Arcs 428 5.2 Right Triangle Trigonometry 442 5.3 Trigonometric Functions of Any Angle 454 5.4 Trigonometric Functions of Real Numbers 461 Mid-Chapter 5 Quiz 472 5.5 Graphs of the Sine and Cosine Functions 473 5.6 Graphs of the Other Trigonometric Functions 481 5.7 Graphing Techniques 491 5.8 Harmonic Motion—An Application of the Sine and Cosine Functions 500 Exploring Concepts with Technology 505 Chapter 5 Test Prep 506 Chapter 5 Review Exercises 510 Chapter 5 Test 512 Cumulative Review Exercises 513