net This page intentionally left blank www.net Intermediate Algebra www.net This page intentionally left blank www.net Intermediate Algebra Sixth Edition Elayn Martin-Gay University of New Orleans Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo www.net Editorial Director, Mathematics: Christine Hoag Acquisitions Editor: Mary Beckwith Executive Content Editor: Kari Heen Associate Content Editor: Christine Whitlock Editorial Assistant: Matthew Summers Executive Director, Development: Carol Trueheart Senior Development Editor: Dawn Nuttall Senior Managing Editor: Karen Wernholm Production Project Manager: Patty Bergin Senior Design Specialist: Heather Scott Associate Director of Design, USHE North and West: Andrea Nix Digital Assets Manager: Marianne Groth Supplements Production Project Manager: Katherine Roz Executive Manager, Course Production: Peter Silvia Media Producer: Audra Walsh Director of Content Development: Rebecca Williams Content Project Supervisor: Janet Szykowny Executive Marketing Manager: Michelle Renda Marketing Assistant: Susan Mai Senior Author Support / Technology Specialist: Joe Vetere Senior Media Buyer: Ginny Michaud Permissions Project Supervisor: Michael Joyce Procurement Specialist: Linda Cox Production Management, Interior Design, Composition, and Answer Art: Integra Text Art: Scientific Illustrators Cover Design and Image: Tamara Newnam 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 Education was aware of a trademark claim, the designations have been printed in initial caps or all caps. Library of Congress Cataloging-in-Publication Data Martin-Gay, K. Elayn Intermediate algebra / Elayn Martin-Gay.9—dc23 2011013318 Copyright © 2013, 2009, 2005, 2002 Pearson Education, Inc.
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1 2 3 4 5 6 7 8 9 10—CRK—15 14 13 12 11 ISBN-10: 0-321-78504-5 www.com ISBN-13: 978-0-321-78504-6 www.net This book is dedicated to students everywhere—and we should all be students. After all, is there anyone among us who really knows too much? Take that hint and continue to learn something new every day of your life. Best of wishes from a fellow student: Elayn Martin-Gay www.net Contents Preface xiv Applications Index xxii CHAPTER REAL NUMBERS AND ALGEBRAIC EXPRESSIONS 1 1 1.1 Tips for Success in Mathematics 2 1.2 Algebraic Expressions and Sets of Numbers 7 1.3 Operations on Real Numbers and Order of Operations 17 Integrated Review—Algebraic Expressions and Operations on Whole Numbers 29 1.4 Properties of Real Numbers and Algebraic Expressions 30 Chapter 1 Vocabulary Check 41 Chapter 1 Highlights 41 Chapter 1 Review 43 Chapter 1 Test 46 CHAPTER EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING 47 2 2.1 Linear Equations in One Variable 48 2.2 An Introduction to Problem Solving 57 2.3 Formulas and Problem Solving 69 2.4 Linear Inequalities and Problem Solving 77 Integrated Review—Linear Equations and Inequalities 88 2.6 Absolute Value Equations 96 2.7 Absolute Value Inequalities 101 Chapter 2 Vocabulary Check 107 Chapter 2 Highlights 107 Chapter 2 Review 111 Chapter 2 Test 113 Chapter 2 Cumulative Review 114 CHAPTER GRAPHS AND FUNCTIONS 116 3 3.2 Introduction to Functions 128 3.3 Graphing Linear Functions 144 3.4 The Slope of a Line 152 3.5 Equations of Lines 165 Integrated Review—Linear Equations in Two Variables 175 3.6 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions 176 3.7 Graphing Linear Inequalities 184 Chapter 3 Vocabulary Check 189 Chapter 3 Highlights 189 Chapter 3 Review 194 Chapter 3 Test 198 Chapter 3 Cumulative Review 199 vi www.net Contents vii CHAPTER SYSTEMS OF EQUATIONS 201 4 4.1 Solving Systems of Linear Equations in Two Variables 202 4.2 Solving Systems of Linear Equations in Three Variables 214 4.3 Systems of Linear Equations and Problem Solving 221 Integrated Review—Systems of Linear Equations 234 4.4 Solving Systems of Equations by Matrices 235 4.5 Systems of Linear Inequalities 241 Chapter 4 Vocabulary Check 244 Chapter 4 Highlights 245 Chapter 4 Review 249 Chapter 4 Test 251 Chapter 4 Cumulative Review 252 CHAPTER EXPONENTS, POLYNOMIALS, AND POLYNOMIAL FUNCTIONS 254 5 5.1 Exponents and Scientific Notation 255 5.2 More Work with Exponents and Scientific Notation 264 5.3 Polynomials and Polynomial Functions 270 5.5 The Greatest Common Factor and Factoring by Grouping 291 5.7 Factoring by Special Products 305 Integrated Review—Operations on Polynomials and Factoring Strategies 310 5.8 Solving Equations by Factoring and Problem Solving 314 Chapter 5 Vocabulary Check 326 Chapter 5 Highlights 327 Chapter 5 Review 329 Chapter 5 Test 332 Chapter 5 Cumulative Review 333 CHAPTER RATIONAL EXPRESSIONS 335 6 6.1 Rational Functions and Multiplying and Dividing Rational Expressions 336 6.2 Adding and Subtracting Rational Expressions 348 6.3 Simplifying Complex Fractions 356 6.4 Dividing Polynomials: Long Division and Synthetic Division 362 6.5 Solving Equations Containing Rational Expressions 372 Integrated Review—Expressions and Equations Containing Rational Expressions 379 6.6 Rational Equations and Problem Solving 381 6.7 Variation and Problem Solving 390 Chapter 6 Vocabulary Check 399 Chapter 6 Highlights 400 Chapter 6 Review 403 Chapter 6 Test 406 Chapter 6 Cumulative Review 407 CHAPTER RATIONAL EXPONENTS, RADICALS, AND COMPLEX NUMBERS 409 7 7.1 Radicals and Radical Functions 410 7.3 Simplifying Radical Expressions 426 7.4 Adding, Subtracting, and Multiplying Radical Expressions 434 7.5 Rationalizing Denominators and Numerators of Radical Expressions 440 Integrated Review—Radicals and Rational Exponents 446 7.6 Radical Equations and Problem Solving 447 7.7 Complex Numbers 457 Chapter 7 Vocabulary Check 464 www.net viii Contents Chapter 7 Highlights 464 Chapter 7 Review 468 Chapter 7 Test 470 Chapter 7 Cumulative Review 471 CHAPTER QUADRATIC EQUATIONS AND FUNCTIONS 474 8 8.1 Solving Quadratic Equations by Completing the Square 475 8.2 Solving Quadratic Equations by the Quadratic Formula 485 8.3 Solving Equations by Using Quadratic Methods 495 Integrated Review—Summary on Solving Quadratic Equations 504 8.4 Nonlinear Inequalities in One Variable 505 8.5 Quadratic Functions and Their Graphs 512 8.6 Further Graphing of Quadratic Functions 520 Chapter 8 Vocabulary Check 528 Chapter 8 Highlights 528 Chapter 8 Review 531 Chapter 8 Test 532 Chapter 8 Cumulative Review 533 CHAPTER EXPONENTIAL AND LOGARITHMIC FUNCTIONS 535 9 9.1 The Algebra of Functions; Composite Functions 536 9.4 Exponential Growth and Decay Functions 561 9.6 Properties of Logarithms 573 Integrated Review—Functions and Properties of Logarithms 579 9.7 Common Logarithms, Natural Logarithms, and Change of Base 580 9.8 Exponential and Logarithmic Equations and Problem Solving 586 Chapter 9 Vocabulary Check 592 Chapter 9 Highlights 593 Chapter 9 Review 596 Chapter 9 Test 598 Chapter 9 Cumulative Review 600 CHAPTER CONIC SECTIONS 602 10 10.1 The Parabola and the Circle 603 10.2 The Ellipse and the Hyperbola 612 Integrated Review—Graphing Conic Sections 619 10.3 Solving Nonlinear Systems of Equations 620 10.4 Nonlinear Inequalities and Systems of Inequalities 625 Chapter 10 Vocabulary Check 629 Chapter 10 Highlights 629 Chapter 10 Review 632 Chapter 10 Test 633 Chapter 10 Cumulative Review 633 CHAPTER SEQUENCES, SERIES, AND THE BINOMIAL THEOREM 635 11 11.2 Arithmetic and Geometric Sequences 640 11.3 Series 648 Integrated Review—Sequences and Series 653 11.4 Partial Sums of Arithmetic and Geometric Sequences 653 11.5 The Binomial Theorem 660 www.net Contents ix Chapter 11 Vocabulary Check 665 Chapter 11 Highlights 665 Chapter 11 Review 667 Chapter 11 Test 669 Chapter 11 Cumulative Review 669 APPENDICES A GEOMETRY 671 B STRETCHING AND COMPRESSING GRAPHS OF ABSOLUTE VALUE FUNCTIONS 678 C SOLVING SYSTEMS OF EQUATIONS USING DETERMINANTS 680 D AN INTRODUCTION TO USING A GRAPHING UTILITY 687 E CONTENTS OF STUDENT RESOURCES 692 Answers to Selected Exercises A1 Index I1 Photo Credits P1 www.net Student Resources These resources, located in the back of the text, give you a variety of tools conveniently located in one place to help you succeed in math. Study Skills Builders Attitude and Study Tips: 1.
Have You Decided to Complete This Course Successfully? 2. Tips for Studying for an Exam 3. What to Do the Day of an Exam 4. Are You Satisfied with Your Performance on a Particular Quiz or Exam? 5.
How Are You Doing? 6. Are You Preparing for Your Final Exam? Organizing Your Work: 7. Learning New Terms 8. Are You Organized? 9.
How Are Your Homework Assignments Going? MyMathLab and MathXL: 11. Tips for Turning in Your Homework on Time 12. Tips for Doing Your Homework Online 13. Organizing Your Work 14.
Getting Help with Your Homework Assignments 15. Tips for Preparing for an Exam 16. How Well Do You Know the Resources Available to You in MyMathLab? Additional Help Inside and Outside Your Textbook: 17. How Well Do You Know Your Textbook? 18.
Are You Familiar with Your Textbook Supplements? 19. Are You Getting All the Mathematics Help That You Need? Bigger Picture–Study Guide Outline Practice Final Exam Answers to Selected Exercises x www.net A New Tool to Help You Succeed Introducing Martin-Gay’s New Student Organizer The new Student Organizer guides you through three important parts of studying effectively–note-taking, practice, and homework. It is designed to help you organize your learning materials and develop the study habits you need to be successful. The Student Organizer includes: • How to prepare for class • Space to take class notes • Step-by-step worked examples • Your Turn exercises (modeled after the examples) • Answers to the Your Turn exercises as well as worked-out solutions via references to the Martin-Gay text and videos • Helpful hints and directions for completing homework assignments A flexible design allows instructors to assign any or all parts of the Student Organizer.
The Student Organizer is available in a loose-leaf, notebook-ready format. It is also available for download in MyMathLab. For more information, please go to www.com/martingay www.com (search Martin-Gay, Intermediate Algebra, Sixth Edition) your Martin-Gay course xi www.net Martin-Gay Video Resources to Help You Succeed Interactive DVD Lecture Series Active Learning at Your Pace Designed for use on your computer or DVD player, these interactive videos include a 15–20 minute lecture for every section in the text as well as Concept Checks, Study Skills Builders, and a Practice Final Exam. Pop-ups Take note of key concepts, terms, and definitions as pop-ups appear through- out each section.
Exercises Know how to do an exercise? Click the “next” arrow to Progress Meter skip ahead or the Monitor your progress through the “back” arrow to lecture and exercises at a glance. review an exercise. Interactive Concept Checks pose questions about key concepts and prompt you to click on an answer. Learn whether your answer is correct and view the full solution.
Study Skills Builders provide tips and suggestions to help you develop effective study habits.net Chapter Test Prep Videos Step-by-step solutions on video for all chapter test exercises from the text. Available via: • Interactive DVD Lecture Series • • AlgebraPrep Apps for the iPhone ™ and iPod Touch ® Your 24/7 Algebra Tutor–Anytime, Anywhere! Choose to take a Practice Test or a MiniTest (designed to take 10 minutes or less). Practice Test exercises provide answer feedback to help you study and self-correct. Step-by-step video solutions give you the guid- ance of an expert tutor whenever you need help.net Preface Intermediate Algebra, Sixth Edition, was written to provide a solid foundation in algebra for students who might not have previous experience in algebra.
Specific care was taken to make sure students have the most up-to-date, relevant text prepara- tion for their next mathematics course or for nonmathematical courses that require an understanding of algebraic fundamentals. I have tried to achieve this by writing a user-friendly text that is keyed to objectives and contains many worked-out examples.