Elementary and Intermediate Algebra, 4th Student Support Edition

1073 Pages·2007·18.8 MB·English

by  Ron Larson

Student Support Edition
Elementary and Intermediate
Algebra: A Combined Course
F O U R T H E D I T I O N
Ron Larson
The Pennsylvania State University
The Behrend College
Robert Hostetler
The Pennsylvania State University
The Behrend College
With the assistance of
Patrick M. Kelly
Mercyhurst College
Houghton Mifflin Company Boston New York
Publisher:Richard Stratton
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Development Editor:Yen Tieu
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Director of Manufacturing:Priscilla Manchester
Cover Design Manager:Anne S. Katzeff
Cover art ©by Dale Chihuly
Wehave included examples and exercises that use real-life data as well as technology output
from a variety of software. This would not have been possible without the help of many people
and organizations. Our wholehearted thanks go to them for all their time and effort.
Trademark acknowledgment: TI is a registered trademark of Texas Instruments,Inc.
Copyright ©2008 by Houghton Mifflin Company. All rights reserved.
This book was originally published in slightly different form as ELEMENTARYAND
INTERMEDIATEALGEBRA,FOURTHEDITION ©2005 by Houghton Mifflin Company.
No part of this work may be reproduced or transmitted in any form or by any means,electronic
or mechanical,including photocopying and recording,or by any information storage or retrieval
system,without the prior written permission of Houghton Mifflin Company unless such copy-
ing is expressly permitted by federal copyright law. Address inquiries to College Permissions,
Houghton MifflinCompany,222 Berkeley Street,Boston,MA 02116-3764.
Printed in the U.S.A.
Library of Congress Catalog Card Number:2006929488
Instructor’s Exam copy:
ISBN 13:978-0-618-75477-9
ISBN 10:0-618-75477-6
For orders,use Student text ISBNs:
ISBN 13:978-0-618-75354-3
ISBN 10:0-618-75354-0
123456789–DOW–09 08 07 06
Contents
Your Guide to Academic Success S1
Your Guide to the Chapters S18
Your Guide to Your Book S44
A Word from the Authors S49
Motivating the Chapter 1
1 The Real Number System 1
1.1 Real Numbers: Order and Absolute 1.5 Exponents,Order of Operations,and
Value 2 Properties of Real Numbers 48
1.2 Adding and Subtracting Integers 12
What Did You Learn? (Chapter Summary) 60
1.3 Multiplying and Dividing Integers 20
Review Exercises 61 Chapter Test 65
Mid-Chapter Quiz 33
1.4 Operations with Rational Numbers 34
Motivating the Chapter 66
2 Fundamentals of Algebra 67
2.1 Writing and Evaluating Algebraic 2.4 Introduction to Equations 105
Expressions 68
What Did You Learn? (Chapter Summary) 116
2.2 Simplifying Algebraic Expressions 78
Review Exercises 117 Chapter Test 121
Mid-Chapter Quiz 90
2.3 Algebra and Problem Solving 91
Motivating the Chapter 122
3 Equations, Inequalities, and Problem Solving 123
3.1 Solving Linear Equations 124 3.6 Linear Inequalities 182
3.2 Equations That Reduce to Linear Form 135 3.7 Absolute Value Equations and
3.3 Problem Solving with Percents 145 Inequalities 196
3.4 Ratios and Proportions 157
What Did You Learn? (Chapter Summary) 206
Mid-Chapter Quiz 168
Review Exercises 207 Chapter Test 211
3.5 Geometric and Scientific Applications 169
Cumulative Test: Chapters 1–3 212
Motivating the Chapter 214
4 Graphs and Functions 215
4.1 Ordered Pairs and Graphs 216 4.5 Equations of Lines 263
4.2 Graphs of Equations in Two Variables 228 4.6 Graphs of Linear Inequalities 275
4.3 Relations,Functions,and Graphs 238
What Did You Learn? (Chapter Summary) 284
Mid-Chapter Quiz 248
Review Exercises 285 Chapter Test 291
4.4 Slope and Graphs of Linear Equations 249
iii
iv Contents
Motivating the Chapter 292
5 Exponents and Polynomials 293
5.1 Integer Exponents and Scientific Notation 294 5.4 Dividing Polynomials and Synthetic
5.2 Adding and Subtracting Polynomials 304 Division 328
Mid-Chapter Quiz 314
What Did You Learn? (Chapter Summary) 338
5.3 Multiplying Polynomials: Special Products 315
Review Exercises 339 Chapter Test 343
Motivating the Chapter 344
6 Factoring and Solving Equations 345
6.1 Factoring Polynomials with Common Factors 346 6.5 Solving Polynomial Equations by Factoring 382
6.2 Factoring Trinomials 354
What Did You Learn? (Chapter Summary) 392
6.3 More About Factoring Trinomials 362
Review Exercises 393 Chapter Test 396
Mid-Chapter Quiz 371
Cumulative Test: Chapters 4–6 397
6.4 Factoring Polynomials with Special Forms 372
Motivating the Chapter 398
7 Rational Expressions, Equations, and Functions 399
7.1 Rational Expressions and Functions 400 7.5 Solving Rational Equations 439
7.2 Multiplying and Dividing Rational 7.6 Applications and Variation 447
Expressions 412
What Did You Learn? (Chapter Summary) 460
7.3 Adding and Subtracting Rational
Review Exercises 461 Chapter Test 465
Expressions 421
Mid-Chapter Quiz 430
7.4 Complex Fractions 431
Motivating the Chapter 466
8 Systems of Equations and Inequalities 467
8.1 Solving Systems of Equations by Graphing 8.5 Determinants and Linear Systems 521
and Substitution 468 8.6 Systems of Linear Inequalities 533
8.2 Solving Systems of Equations by Elimination 485
What Did You Learn? (Chapter Summary) 543
8.3 Linear Systems in Three Variables 495
Review Exercises 544 Chapter Test 549
Mid-Chapter Quiz 507
8.4 Matrices and Linear Systems 508
Contents v
Motivating the Chapter 550
9 Radicals and Complex Numbers 551
9.1 Radicals and Rational Exponents 552 9.6 Complex Numbers 595
9.2 Simplifying Radical Expressions 563
What Did You Learn? (Chapter Summary) 604
9.3 Adding and Subtracting Radical Expressions 570
Review Exercises 605 Chapter Test 609
Mid-Chapter Quiz 576
Cumulative Test: Chapters 7–9 610
9.4 Multiplying and Dividing Radical Expressions 577
9.5 Radical Equations and Applications 585
Motivating the Chapter 612
10 Quadratic Equations, Functions, and Inequalities 613
10.1 Solving Quadratic Equations: Factoring and 10.5 Applications of Quadratic Equations 652
Special Forms 614 10.6 Quadratic and Rational Inequalities 663
10.2 Completing the Square 623
What Did You Learn? (Chapter Summary) 673
10.3 The Quadratic Formula 631
Review Exercises 674 Chapter Test 677
Mid-Chapter Quiz 641
10.4 Graphs of Quadratic Functions 642
Motivating the Chapter 678
11 Exponential and Logarithmic Functions 679
11.1 Exponential Functions 680 11.5 Solving Exponential and Logarithmic
11.2 Composite and Inverse Functions 693 Equations 728
11.3 Logarithmic Functions 707 11.6 Applications 738
Mid-Chapter Quiz 718
What Did You Learn? (Chapter Summary) 749
11.4 Properties of Logarithms 719
Review Exercises 750 Chapter Test 755
Motivating the Chapter 756
12 Conics 757
12.1 Circles and Parabolas 758 What Did You Learn? (Chapter Summary) 800
12.2 Ellipses 770 Review Exercises 801 Chapter Test 805
Mid-Chapter Quiz 780 Cumulative Test: Chapters 10–12 806
12.3 Hyperbolas 781
12.4 Solving Nonlinear Systems of Equations 789
vi Contents
Motivating the Chapter 808
13 Sequences, Series, and the Binomial Theorem 809
13.1 Sequences and Series 810 What Did You Learn? (Chapter Summary) 849
13.2 Arithmetic Sequences 821 Review Exercises 850 Chapter Test 853
Mid-Chapter Quiz 830
13.3 Geometric Sequences and Series 831
13.4 The Binomial Theorem 841
Appendices
Appendix A Review of Elementary Algebra Topics A1
A.1 The Real Number System A1
A.2 Fundamentals of Algebra A6
A.3 Equations,Inequalities,and Problem Solving A9
A.4 Graphs and Functions A16
A.5 Exponents and Polynomials A24
A.6 Factoring and Solving Equations A32
Appendix B Introduction to Graphing Calculators A40
Appendix C Further Concepts in Geometry*
C.1 Exploring Congruence and Similarity
C.2 Angles
Appendix D Further Concepts in Statistics*
Appendix E Introduction to Logic*
E.1 Statements and Truth Tables
E.2 Implications,Quantifiers,and Venn Diagrams
E.3 Logical Arguments
Appendix F Counting Principles*
Appendix G Probability*
Answers to Reviews,Odd-Numbered Exercises,Quizzes,and Tests A47
Index of Applications A145
Index A150
*Appendices C,D,E,F,and G are available on the textbook website and Eduspace®.
To access the appendices online,go to college.hmco.com/pic/larsonEIASSE4e.
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Your Guide to Success in Algebra is designed to help you to
effectively prepare,plan,and track your progress in your algebra course.
It includes:
Your Guide to Academic Success
Review your math study skills,discover your own learning style,develop
strategies for test-taking, studying and time management, track your
course progress,and get the most out of your textbook and study aids.
Your Guide to the Chapters
Track your progress in each chapter’s topics and learning objectives.
A checklist is provided for you to monitor your use of the study aids
available for that chapter.
Your Guide to Your Book
Take a look at the tools your text offers, including examples, study and
technology tips,graphics,and end of chapter material.
Removable Study Cards
Check out these convenient cards within your text for quick access to
common formulas, algebraic properties, conversions, geometric formula
study sheets,and more.
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AAccaaddeemmiicc SSuucccceessss
Hello and welcome! The purpose of this Student Support Edition is to provide
you with the tools you need to be successful in your algebra course.Along with
general tips on good study habits,you will find information on the best way to
use this textbook program based on your individual strengths.Take time to
work through these pages,and you will learn how to succeed in your algebra
course and other math courses that may follow.
“There are no secrets to success.It is the result of preparation,hard
work,and learning from failure.” — Colin Powell
Math is no different.You will be successful in math—and in any other course,
for that matter—if you prepare for class,do your homework,and study for your
tests.Shortcuts simply don’t work! Plan to attend class,ask questions,do your
homework,study regularly,and manage your time appropriately.Give yourself
the chance to learn!
Review the Basics of Your Algebra Course
Before you head off to class,make sure you know the name of the instructor,
where the class is located,and when the class is held.If you haven’t been to the
classroom or building before,make a practice run before the first day of class.
Course Name and Number:_____________________________________
Course Location:______________________________________________
Course Time:_________________________________________________
Instructor:___________________________________________________
Email: ______________________________________________________
Office Location: ______________________________________________
Office Hours: ________________________________________________
Makeuse of any resources on campus,such as computer labs,video labs,and
tutoring centers. If there is a tutoring center available, find out where it is
located and when it is open.
S2
Your Guide to Academic Success S3
Tutoring Center Location: ______________________________________
Tutoring Center Hours:_________________________________________
Are you planning to take an online course? If so,do you know how to access
the course? What are the minimum requirements for a computer? Be sure to
address these questions before the first day of class.
Next,familiarize yourself with the textbook before going to class.Look at
the following items.
Get to Know Your Textbook
Assignment Log
The assignment log is located opposite the inside front cover of the textbook.
Use this log to record each homework assignment along with any relevant
notes or page numbers.
Your Guide to the Chapters
Located after Your Guide to Academic Successare detailed guides to each chapter.
On these pages, you will find a summary of the topics (objectives)
covered in each chapter,along with relevant key terms that you can use to help
study for quizzes and tests.There is also a place to record when you have
completed your assignments,the Mid-Chapter Quiz,the Chapter Review,the
Chapter Test,and the Cumulative Test,all of which are important steps in the
process of studying and preparing for exams.Remember:In order to succeed
in your algebra course,you must keep up with your assignments.
Your Guide to Your Textbook
Look through the textbook to get a feel for what it looks like and what types of
features are included. Notice the four Algebra Study Cards—in the middle
of the book—with the key definitions, formulas, and equations that are
fundamental to this course.Tear these out of the book and use them as a quick
reference whenever and wherever you study.
Discover Your Learning Style
The following,“Claim Your Multiple Intelligences”is an excerpt from Becoming a
Master Student by Dave Ellis.The article will help you discover your particular
learning styles and give you tips on how best to utilize them when studying.
Claim Your Multiple Intelligences*
People often think that being smart means the same thing as having a high
IQ, and that having a high IQ automatically leads to success. However,
psychologists are finding that IQ scores do not always foretell which students
will do well in academic settings—or after they graduate.