net Innovative Technology to Help You Succeed MyMathLab can improve any learning environment—whether you are taking a lab-based, hybrid, fully online, or a traditional lecture-style course. INTERACTIVE FIGURES Math comes alive with new Interactive Figures in MyMathLab! Your instructor may choose to assign assessment questions that are written to accompany each figure. This interaction will lead you to fully understand key mathematical concepts in a hands-on, engaging way. A HISTORY OF SUCCESS Results show that you can improve your grade by using the videos, animations, interactive figures, step-by-step examples, and personalized feedback in MyMathLab.
To see the growing list of case studies for yourself, visit www.com/success-stories www.net Prepare for Class “Read the Book” Feature Description Benefit Page Every chapter begins with…. Chapter Opening Each chapter begins with a current The Article describes a real situation. The 398, 501 Article & Project article and ends with a related project. Project lets you apply what you learned to solve a related problem.
NEW! The projects allow for the integration of The projects allow the opportunity 398, 501 Internet-based spreadsheet technology that students for students to collaborate and use Projects will need to be a productive member of mathematics to deal with issues that come the workforce. up in their lives. Every section begins with…. Learning Each section begins with a list of These focus your studying by emphasizing 419 Objectives objectives.
Objectives also appear in the what’s most important and where to find it. text where the objective is covered. 1 Most sections contain… PREPARING FOR Most sections begin with a list of key Ever forget what you’ve learned? This feature 419 THIS SECTION concepts to review with page numbers. highlights previously learned material to be used in this section.
Review it, and you’ll always be prepared to move forward. Now Work the Problems that assess whether you have Not sure you need the Preparing for This 419, 430 ‘Are You the prerequisite knowledge for the Section review? Work the ‘Are You Prepared?’ Prepared?’ upcoming section. If you get one wrong, you’ll know Problems exactly what you need to review and where to review it! “Now Work ” These follow most examples and direct We learn best by doing. You’ll solidify your 428 PROBLEMS you to a related exercise.
understanding of examples if you try a similar problem right away, to be sure you understand what you’ve just read. WARNING Warnings are provided in the text. These point out common mistakes 453 and help you to avoid them. Explorations and These represent graphing utility You will obtain a deeper and more intuitive 252, 425 Seeing the Concept activities to foreshadow a concept or understanding of theorems and definitions.
solidify a concept just presented. These provide alternative descriptions of Does math ever look foreign to you? 421 In Words select definitions and theorems. This feature translates math into plain English. Calculus Icon These appear next to information Pay attention -- if you spend extra 365 essential for the study of calculus.
time now, you’ll do better later! Showcase These examples provide “how-to” With each step presented on the left and 337–338 EXAMPLES instruction by offering a guided, step- the mathematics displayed on the right, by-step approach to solving a problem. students can immediately see how each step is employed. Model It! Marked with. These are examples It is rare for a problem to come in the form, 444, 473 Examples and and problems that require you to “Solve the following equation”.
Rather, the Problems build a mathematical model from equation must be developed based on an either a verbal description or data. explanation of the problem. These problems The homework Model It! problems are require you to develop models that will allow marked by purple numbers. you to describe the problem mathematically and suggest a solution to the problem.net Practice “Work the Problems” Feature Description Benefit Page “Assess Your Understanding” contains a variety of problems at the end of each section.
‘Are You These assess your retention of the Do you always remember what you’ve 419, 430 Prepared?’ prerequisite material you’ll need. learned? Working these problems Problems Answers are given at the end of the is the best way to find out. This feature is related If you get one wrong, you’ll know exactly to the Preparing for This Section feature. what you need to review and where to review it! Concepts and These short-answer questions, mainly It is difficult to learn math without knowing 431 Vocabulary Fill-in-the-Blank and True/False items, the language of mathematics.
These assess your understanding of key problems test your understanding of definitions and concepts in the current the formulas and vocabulary. Skill Correlated to section examples, these It’s important to dig in and develop 431–433 Building problems provide straightforward your skills. These problems provide you practice. with ample practice to do so.
Mixed These problems offer comprehensive Learning mathematics is a building process. 433 Practice assessment of the skills learned in the Many concepts are interrelated. These section by asking problems that relate to problems help you see how mathematics more than one concept or objective. builds on itself and also see how the These problems may also require you to concepts tie together.
utilize skills learned in previous sections. Applications These problems allow you to apply You will see that the material 433–435 and your skills to real-world problems. learned within the section has Extensions These problems also allow you to many uses in everyday life. extend concepts leamed in the section.
Explaining “Discussion and Writing” problems To verbalize an idea, or to describe 436 Concepts: are colored red. These support it clearly in writing, shows real Discussion class discussion, verbalization of understanding. These problems nurture and mathematical ideas, and writing and that understanding. Many are Writing research projects.
challenging but you’ll get out what you put in. NEW! In selected exercise sets, applets The applets allow students to interact with 345–346 Interactive are provided to give a “hands-on” mathematics in an active learning environment. By exploring a variety of scenarios, the student is able to visualize the mathematics and develop a deeper conceptual understanding of the material. “Now Work ” Many examples refer you to a related If you get stuck while working 429 PROBLEMS homework problem.
These related problems, look for the closest problems are marked by a pencil and Now Work problem and refer back yellow numbers. to the related example to see if it helps. Chapter Every chapter concludes with a Work these problems to verify you 495–499 Review comprehensive list of exercises to understand all the skills and concepts of Problems pratice. Use the list of objectives to the chapter.
Think of it as a comprehensive determine the objective and examples review of the chapter. that correspond to the problems.net Review “Study for Quizzes and Tests” Feature Description Benefit Page Chapter Reviews at the end of each chapter contain… “Things to Know” A detailed list of important theorems, Review these and you’ll know the most 494–495 formulas, and definitions from the important material in the chapter! chapter. “You should be able to…” Contains a complete list of objectives Do the recommended exercises and 495–496 by section, examples that illustrate the you’ll have mastery over the key objective, and practice exercises that test material. If you get something wrong, your understanding of the objective.
review the suggested examples and page numbers and try again. Review Exercises These provide comprehensive review Practice makes perfect. These problems 496–499 and practice of key skills, matched to the combine exercises from all sections, Learning Objectives for each section. giving you a comprehensive review in one place.
CHAPTER TEST About 15–20 problems that can be taken Be prepared. Take the sample practice 499–500 as a Chapter Test. Be sure to take the test under test conditions. This will get Chapter Test under test conditions—no you ready for your instructor’s test.
If you notes! get a problem wrong, watch the Chapter Test Prep video. CUMULATIVE REVIEW These problem sets appear at the These are really important. They will 500 end of each chapter, beginning with ensure that you are not forgetting Chapter 2. They combine problems from anything as you go.
These will go a long previous chapters, providing an ongoing way toward keeping you constantly cumulative review. primed for the final exam. CHAPTER PROJECTS The Chapter Project applies what you’ve The Project gives you an opportunity 501 learned in the chapter. Additional to apply what you’ve learned in projects are available on the Instructor’s the chapter to solve a problem Resource Center (IRC).
related to the opening article. If your instructor allows, these make excellent opportunities to work in a group, which is often the best way of learning math. NEW! In selected chapters, a web-based The projects allow the opportunity 501 Internet-based Projects project is given. for students to collaborate and use mathematics to deal with issues that come up in their lives.net This page intentionally left blank www.net ALGEBRA & TRIGONOMETRY Enhanced with Graphing Utilities Sixth Edition Michael Sullivan Chicago State University Michael Sullivan, III Joliet Junior College Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo www.net Editor in Chief: Anne Kelly Sponsoring Editor: Dawn Murrin Assistant Editor: Joseph Colella Executive Marketing Manager: Roxanne McCarley Marketing Manager: Peggy Sue Lucas Marketing Assistant: Justine Goulart Senior Managing Editor: Karen Wernholm Associate Managing Editor: Tamela Ambush Senior Production Project Manager: Peggy McMahon Procurement Manager/Boston: Evelyn Beaton Procurement Specialist: Debbie Rossi Procurement Media Specialist: Ginny Michaud Senior Author Support/Technology Specialist: Joe Vetere Associate Director of Design, USHE North and West: Andrea Nix Senior Design Specialist: Heather Scott Interior and Cover Design: Tamara Newnam Cover Image (background): iStockphoto/Simfo Image Manager:/Image Management Services: Rachel Youdelman Photo Research: PreMedia Global Permissions Project Manager: Michael Joyce Media Producer: Christina Maestri Software Development: Kristina Evans, Mary Durnwald, and Marty Wright Full-Service Project Management: Cenveo Publisher Services/Nesbitt Graphics, Inc.
Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this text appear on page xxviii of the book Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and Pearson was aware of a trademark claim, the designations have been printed in initial caps or all caps. Microsoft® and Windows® are registered trademarks of the Microsoft Corporation in the U. and other countries.
Screen shots and icons reprinted with permission from the Microsoft Corporation. This book is not sponsored or endorsed by or affiliated with the Microsoft Corporation. Library of Congress Cataloging-in-Publication Data Sullivan, Michael, 1942- Algebra & trigonometry : enhanced with graphing utilities/Michael Sullivan, Michael Sullivan, III. Includes bibliographical references and index.
Algebra–Graphic methods. Trigonometry–Graphic methods. Sullivan, Michael, 1967 July 2- II. Title: Algebra and trigonometry.13–dc23 2011024234 Copyright ©2013, 2009, 2006, 2003, 2000 Pearson Education, Inc.
All rights reserved. Manufactured in the United States of America. This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake Street, Upper Saddle River, New Jersey 07458, or you may fax your request to 201-236-3290.
1 2 3 4 5 6 7 8 9 10—CRK—15 14 13 12 11 ISBN-10: 0-321-78483-9 ISBN-13: 978-0-321-78483-4 www.net For the Family Katy (Murphy) and Pat Shannon, Patrick, Ryan Mike and Yola Michael, Kevin, Marissa Dan and Sheila Maeve, Sean, Nolan Colleen (O’Hara) and Bill Kaleigh, Billy, Timmy www.net This page intentionally left blank www.net Contents To the Student xii Preface to the Instructor xiv Applications Index xxi Photo Credits xxviii R Review 1 R.8 nth Roots; Rational Exponents 73 1 Graphs, Equations, and Inequalities 81 1.
