Elementary & Intermediate Algebra, 3rd Edition

978 Pages·2011·14.32 MB·English

by  George Woodbury

Annotated Instructor’s Edition
Elementary
and
Intermediate Algebra
Third Edition
George Woodbury
College of the Sequoias
Addison-Wesley
Boston Columbus Indianapolis New York San Francisco Upper Saddle River
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Library of Congress Cataloging-in-Publication Data
Woodbury,George,1967-
Elementary and intermediate algebra / George Woodbury.-- 3rd ed.
p.cm.
Includes index.
ISBN-13:978-0-321-66548-5 (student ed.)
ISBN-10:0-321-66548-1 (student ed.)
ISBN-13:978-0-321-66584-3 (instructor ed.)
ISBN-10:0-321-66584-8 (instructor ed.)
1. Algebra--Textbooks. I.Title.
QA152.3.W66 2012
512.9--dc22 2010002670
Copyright © 2012 Pearson Education,Inc.,publishing as Addison-Wesley,75 Arlington Street,
Boston,MA 02116.All rights reserved.Manufactured in the United States of America.This pub-
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aware of a trademark claim,the designations have been printed in initial caps or all caps.
ISBN-10: 0-321-66548-1
ISBN-13:978-0-321-66548-5
To Tina, Dylan, and Alycia
You make everything meaningful and worthwhile—
yesterday, today, and tomorrow.
Contents
Preface viii
1
Review of Real Numbers 1
1.1 Integers, Opposites, and Absolute Values 1
1.2 Operations with Integers 6
1.3 Fractions 15
1.4 Operations with Fractions 20
1.5 Decimals and Percents 27
1.6 Basic Statistics 32
1.7 Exponents and Order of Operations 43
1.8 Introduction to Algebra 47
Chapter 1 Summary 55
Chapter 1 Review 60
Chapter 1 Test 62
Mathematicians in History 62
2
Linear Equations 63
2.1 Introduction to Linear Equations 63
2.2 Solving Linear Equations: A General Strategy 70
2.3 Problem Solving; Applications of Linear Equations 79
2.4 Applications Involving Percentages; Ratio and Proportion 90
2.5 Linear Inequalities 101
Chapter 2 Summary 111
Chapter 2 Review 115
Chapter 2 Test 116
Mathematicians in History 117
3
Graphing Linear Equations 118
3.1 The Rectangular Coordinate System; Equations in Two Variables 118
3.2 Graphing Linear Equations and Their Intercepts 128
3.3 Slope of a Line 140
3.4 Linear Functions 153
3.5 Parallel and Perpendicular Lines 162
3.6 Equations of Lines 168
3.7 Linear Inequalities 176
Chapter 3 Summary 187
Chapter 3 Review 193
Chapter 3 Test 196
Mathematicians in History 197
4
Systems of Equations 198
4.1 Systems of Linear Equations; Solving Systems by Graphing 198
4.2 Solving Systems of Equations by Using the Substitution Method 207
4.3 Solving Systems of Equations by Using the Addition Method 214
4.4 Applications of Systems of Equations 224
4.5 Systems of Linear Inequalities 234
iv
Contents v
Chapter 4 Summary 241
Chapter 4 Review 245
Chapter 4 Test 247
Mathematicians in History 248
Chapters 1–4 Cumulative Review 249
5
Exponents and Polynomials 251
5.1 Exponents 251
5.2 Negative Exponents; Scientific Notation 260
5.3 Polynomials; Addition and Subtraction of Polynomials 268
5.4 Multiplying Polynomials 275
5.5 Dividing of Polynomials 281
Chapter 5 Summary 289
Chapter 5 Review 292
Chapter 5 Test 293
Mathematicians in History 294
6
Factoring and Quadratic Equations 295
6.1 An Introduction to Factoring; The Greatest Common Factor;
Factoring by Grouping 295
6.2 Factoring Trinomials of the Form x2 + bx + c 302
6.3 Factoring Trinomials of the Form ax2 + bx + c, where a Z 1 308
6.4 Factoring Special Binomials 313
6.5 Factoring Polynomials: A General Strategy 319
6.6 Solving Quadratic Equations by Factoring 324
6.7 Quadratic Functions 332
6.8 Applications of Quadratic Equations and Quadratic Functions 338
Chapter 6 Summary 347
Chapter 6 Review 351
Chapter 6 Test 352
Mathematicians in History 353
7
Rational Expressions and Equations 354
7.1 Rational Expressions and Functions 354
7.2 Multiplication and Division of Rational Expressions 363
7.3 Addition and Subtraction of Rational Expressions That
Have the Same Denominator 369
7.4 Addition and Subtraction of Rational Expressions That
Have Different Denominators 375
7.5 Complex Fractions 375
7.6 Rational Equations 388
7.7 Applications of Rational Equations 395
Chapter 7 Summary 407
Chapter 7 Review 413
Chapter 7 Test 415
Mathematicians in History 416
Chapters 5–7 Cumulative Review 417
vi Contents
8
A Transition 419
8.1 Linear Equations and Absolute Value Equations 419
8.2 Linear Inequalities and Absolute Value Inequalities 426
8.3 Graphing Linear Equations and Functions;
Graphing Absolute Value Functions 436
8.4 Review of Factoring; Quadratic Equations and Rational Equations 450
8.5 Systems of Equations (Two Equations in Two Unknowns,
Three Equations in Three Unknowns) 458
Chapter 8 Summary 472
Chapter 8 Review 477
Chapter 8 Test 479
Mathematicians in History 480
9
Radical Expressions and Equations 481
9.1 Square Roots; Radical Notation 481
9.2 Rational Exponents 490
9.3 Simplifying, Adding, and Subtracting Radical Expressions 495
9.4 Multiplying and Dividing Radical Expressions 500
9.5 Radical Equations and Applications of Radical Equations 509
9.6 The Complex Numbers 518
Chapter 9 Summary 528
Chapter 9 Review 533
Chapter 9 Test 534
Mathematicians in History 535
10
Quadratic Equations 536
10.1 Solving Quadratic Equations by Extracting Square Roots;
Completing the Square 536
10.2 The Quadratic Formula 547
10.3 Equations That Are Quadratic in Form 557
10.4 Graphing Quadratic Equations 565
10.5 Applications Using Quadratic Equations 575
10.6 Quadratic and Rational Inequalities 582
Chapter 10 Summary 594
Chapter 10 Review 600
Chapter 10 Test 602
Mathematicians in History 603
11
Functions 604
11.1 Review of Functions 604
11.2 Linear Functions 614
11.3 Quadratic Functions 622
11.4 Other Functions and Their Graphs 634
11.5 The Algebra of Functions 648
11.6 Inverse Functions 657
Chapter 11 Summary 668
Chapter 11 Review 675
Chapter 11 Test 680
Mathematicians in History 681
Chapters 8–11 Cumulative Review 682
Contents vii
12
Logarithmic and Exponential Functions 685
12.1 Exponential Functions 685
12.2 Logarithmic Functions 695
12.3 Properties of Logarithms 706
12.4 Exponential and Logarithmic Equations 715
12.5 Applications of Exponential and Logarithmic Functions 725
12.6 Graphing Exponential and Logarithmic Functions 736
Chapter 12 Summary 748
Chapter 12 Review 754
Chapter 12 Test 755
Mathematicians in History 756
13
Conic Sections 757
13.1 Parabolas 757
13.2 Circles 771
13.3 Ellipses 784
13.4 Hyperbolas 797
13.5 Nonlinear Systems of Equations 813
Chapter 13 Summary 823
Chapter 13 Review 829
Chapter 13 Test 833
Mathematicians in History 835
14
Sequences, Series, and the Binomial Theorem 836
14.1 Sequences and Series 836
14.2 Arithmetic Sequences and Series 843
14.3 Geometric Sequences and Series 849
14.4 The Binomial Theorem 857
Chapter 14 Summary 863
Chapter 14 Review 866
Chapter 14 Test 867
Mathematicians in History 868
Chapters 12–14 Cumulative Review 869
Appendixes A-1
A-1 Synthetic Division A-1
A-2 Using Matrices to Solve Systems of Equations A-4
Answers to Selected Exercises AN-1
Index of Applications I-1
Index I-4
Photo Credits PC-1
Preface
Dear Instructors,
Developmental mathematics is our students’ gateway to academic success and a
better life. I wrote this textbook with my own students and their success in mind.
I hope you find that this textbook provides you with the necessary tools to help
your students learn and increase their understanding of math.
I wrote this textbook as a combined algebra textbook from the ground up,
rather than piecing together two separate elementary algebra and intermediate
algebra textbooks. My goal was to create one book that would take students
through elementary and intermediate algebra in a seamless fashion, eliminating
much of the overlap between the two courses. The centerpiece of this strategy
is Chapter 8: A Transition. This chapter reviews essential elementary algebra
topics while quickly extending them to new intermediate algebra topics.
My approach to functions is “Early and Often.” By introducing functions in
Chapter 3, and including them in nearly every subsequent chapter, I give
elementary algebra students plenty of time to get accustomed to function
notation, evaluating functions, and graphing functions before the difficult
topics of composition of functions and inverse functions.
I have been using MyMathLab® in my classes for over ten years, and I have
personally witnessed the power of MyMathLab® to help students learn and
understand mathematics. In fact, when I first decided to pursue writing this
textbook, I chose Pearson as my publisher because I was such a strong
advocate of incorporating MyMathLab® into developmental math classes.
As I have traveled throughout the country and have had the chance to
speak with instructors, it has become clear to me that while it is quite easy for
instructors to get started with MyMathLab®, many instructors needed to
develop a strategy to effectively incorporate MyMathLab® into their classes to
promote learning and understanding. Common questions include the
following:
• How long should a homework assignment be?
• Is homework sufficient, or should I incorporate quizzes?
• What portion of the overall grade should come from MyMathLab®?
• How do I incorporate MyMathLab® into a traditional course? Into an online
course?
To answer those and other questions, I have created a manual for instructors that
focuses on strategies for successfully incorporating MyMathLab®into a course.
Inaddition, I address many practical how-to questions. The manual is intended
to help new instructors get started with MyMathLab®while at the same time
helping those instructors who are experienced with MyMathLab®to use it in a
more effective manner.
If you have questions or want to explore MyMathLab® further, feel free to
visit my website: www.georgewoodbury.com. There you will find many helpful
articles. You also can access my blog and e-mail me through the contact page
or get in touch with me via Twitter or Facebook.
Best of luck this semester!
viii
Preface ix
NEW TO THIS EDITION
Responses from instructors and students have led to adjustments in the coverage
and distribution of certain topics and encouraged expansion of the book’s examples,
exercises,and updated applications.
Content and Organization
• A new section covers basic statistics (Section 1.6).
• Dimensional analysis is introduced in Section 2.4 (Applications Involving
Percentages;Ratio and Proportion),and additional coverage can be found online.
• The presentation of topics and objectives in Section 7.1 (Rational Expressions
and Functions) has been reorganized.
• A general strategy for solving quadratic equations was added to Chapter 10
(Section 10.2,The Quadratic Formula).
• The presentation of topics in Section 10.4 (Graphing Quadratic Equations) was
revised to clarify graphing quadratic equations in standard form.
• Starting in Section 11.3 (Quadratic Functions),a new approach to graphing that
focuses on shifts and transitions instead of a point-plotting method is used
throughout Chapters 11–13.
• Sections 12.1 (Exponential Functions) and 12.2 (Logarithmic Functions) focus on
the basic graphs of f1x2 = bxand f1x2 = log x.The graphs of f1x2 = bx-h + k
b
and f1x2 = log 1x - h2 + k are then covered completely in Section 12.6
b
(Graphing Exponential and Logarithmic Functions).
• The Chapter Summaries have been expanded to a two-column procedure/example
format.
Examples, Exercises, and Applications
• Additional Mixed Practice problems have been added throughout the text.
• Section 3.1 (The Rectangular Coordinate System; Equations in Two Variables)
now has an additional example and exercises that use real-world data for plotting
ordered pairs.
• The factoring exercises in Section 6.5 (Factoring Polynomials:A General Strategy)
have been restructured.
• The coverage of factoring polynomials in Section 8.4 (Review of Factoring;
Quadratic Equations and Rational Equations) has been expanded with additional
examples and a General Factoring Strategy.
• An example that uses systems of two linear equations in two unknowns to solve
real-world problems was added to Section 8.5 (Systems of Equations, Two
Equations in Two Unknowns,Three Equations in Three Unknowns).
• New application problems on Body Surface Area (BSA) and distance to the
horizon were added to Section 9.5 (Radical Equations and Applications of Radical
Equations).
Resources for the Student and Instructor
• George Woodbury’s Guide to MyMathLab®provides instructors with helpful ways
to make the most out of their MyMathLab® experience. New and experienced
users alike will benefit from George Woodbury’s tips for implementing the many
useful features available through MyMathLab®.
• The new Guide to Skills and Concepts, specifically designed for the Woodbury
series,includes additional exercises and resources for every section of the text to
help students make the transition from acquiring skills to learning concepts.