Elementary and Intermediate Algebra, 4th Edition

1355 Pages·2008·51.79 MB·English

by  Alan S. Tussy

ELEMENTARY AND
INTERMEDIATE
ALGEBRA
FOURTH
EDITION
Alan S. Tussy ■ R. David Gustafson
Citrus College Rock Valley College
Christo
© 1972
Shrunk
Harry
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Elementary and Intermediate Algebra, © 2009, 2005Brooks/Cole, Cengage Learning
Fourth Edition
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Alan S. Tussy, R. David Gustafson
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1 2 3 4 5 6 7 12 11 10 09 08
In memory of my mother, Jeanene,
and in honor of my dad, Bill.
—AST
In memory of my teacher and mentor,
Professor John Finch.
—RDG
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CONTENTS
1
AN INTRODUCTION TO ALGEBRA 1
1.1 Introducing the Language of Algebra 2
1.2 Fractions 11
1.3 The Real Numbers 25
1.4 Adding Real Numbers; Properties of Addition 35
1.5 Subtracting Real Numbers 44
1.6 Multiplying and Dividing Real Numbers; Multiplication
and Division Properties 51
1.7 Exponents and Order of Operations 62
1.8 Algebraic Expressions 74
1.9 Simplifying Algebraic Expressions Using Properties of Real Numbers 85
Chapter Summary and Review 96
Chapter Test 105
Group Project 106
2
EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING 107
2.1 Solving Equations Using Properties of Equality 108
2.2 More about Solving Equations 119
2.3 Applications of Percent 129
2.4 Formulas 138
2.5 Problem Solving 152
2.6 More about Problem Solving 162
2.7 Solving Inequalities 173
Chapter Summary and Review 187
Chapter Test 194
Group Project 196
3
GRAPHING LINEAR EQUATIONS AND INEQUALITIES IN TWO
VARIABLES; FUNCTIONS 197
3.1 Graphing Using the Rectangular CoordinateSystem 198
3.2 Graphing Linear Equations 208
3.3 Intercepts 220
3.4 Slope and Rate of Change 232
3.5 Slope–Intercept Form 247
3.6 Point–Slope Form 258
3.7 Graphing Linear Inequalities 268
3.8 An Introduction to Functions 279
Chapter Summary and Review 293
Chapter Test 302
Group Project 304
Cumulative Review 305
v
vi CONTENTS
4
SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES 307
4.1 Solving Systems of Equations by Graphing 308
4.2 Solving Systems of Equations by Substitution 319
4.3 Solving Systems of Equations by Elimination (Addition) 330
4.4 Problem Solving Using Systems of Equations 341
4.5 Solving Systems of Linear Inequalities 356
Chapter Summary and Review 366
Chapter Test 372
Group Project 373
5
EXPONENTS AND POLYNOMIALS 375
5.1 Rules for Exponents 376
5.2 Zero and Negative Exponents 389
5.3 Scientific Notation 399
5.4 Polynomials 406
5.5 Adding and Subtracting Polynomials 416
5.6 Multiplying Polynomials 427
5.7 Special Products 437
5.8 Dividing Polynomials 446
Chapter Summary and Review 456
Chapter Test 464
Group Project 465
Cumulative Review 466
6
FACTORING AND QUADRATIC EQUATIONS 469
6.1 The Greatest Common Factor; Factoring byGrouping 470
6.2 Factoring Trinomials of the Form x2(cid:2)bx(cid:2)c 481
6.3 Factoring Trinomials of the Form ax2(cid:2)bx(cid:2)c 493
6.4 Factoring Perfect-Square Trinomials and the Differences of Two Squares 504
6.5 Factoring the Sum and Difference of TwoCubes 512
6.6 A Factoring Strategy 517
6.7 Solving Quadratic Equations by Factoring 522
6.8 Applications of Quadratic Equations 531
Chapter Summary and Review 540
Chapter Test 547
Group Project 549
7
RATIONAL EXPRESSIONS AND EQUATIONS 551
7.1 Simplifying Rational Expressions 552
7.2 Multiplying and Dividing RationalExpressions 562
7.3 Adding and Subtracting with Like Denominators; Least Common
Denominators 572
7.4 Adding and Subtracting with Unlike Denominators 582
7.5 Simplifying Complex Fractions 591
7.6 Solving Rational Equations 600
7.7 Problem Solving Using Rational Equations 609
7.8 Proportions and Similar Triangles 620
Chapter Summary and Review 632
Chapter Test 640
Group Project 642
Cumulative Review 642
CONTENTS vii
8
TRANSITION TO INTERMEDIATE ALGEBRA 645
8.1 Review of Solving Linear Equations, Formulas, and Linear Inequalities 646
8.2 Solving Compound Inequalities 660
8.3 Solving Absolute Value Equations and Inequalities 672
8.4 Review of Factoring Methods: GCF, Grouping, Trinomials 685
8.5 Review of Factoring Methods: The Difference of Two Squares; the Sum and
Difference of Two Cubes 697
8.6 Review of RationalExpressions and Rational Equations 705
8.7 Review of Linear Equations in Two Variables 720
8.8 Functions 736
8.9 Variation 756
Chapter Summary and Review 765
Chapter Test 781
Group Project 783
Cumulative Review 784
9
RADICAL EXPRESSIONS AND EQUATIONS 787
9.1 Radical Expressions and Radical Functions 788
9.2 Rational Exponents 804
9.3 Simplifying and Combining Radical Expressions 817
9.4 Multiplying and Dividing Radical Expressions 829
9.5 Solving Radical Equations 842
9.6 Geometric Applications of Radicals 854
9.7 Complex Numbers 867
Chapter Summary and Review 880
Chapter Test 889
Group Project 891
10
QUADRATIC EQUATIONS, FUNCTIONS, AND INEQUALITIES 893
10.1 The Square Root Property and Completing the Square 894
10.2 The Quadratic Formula 907
10.3 The Discriminant and Equations That Can Be Written in Quadratic Form 919
10.4 Quadratic Functions and Their Graphs 929
10.5 Quadratic and Other Nonlinear Inequalities 945
Chapter Summary and Review 957
Chapter Test 964
Group Project 966
Cumulative Review 967
11
EXPONENTIAL AND LOGARITHMIC FUNCTIONS 971
11.1 Algebra and Composition of Functions 972
11.2 Inverse Functions 984
11.3 Exponential Functions 996
11.4 Base-eExponential Functions 1012
11.5 Logarithmic Functions 1021
11.6 Base-eLogarithmic Functions 1035
11.7 Properties of Logarithms 1043
11.8 Exponential and Logarithmic Equations 1055
Chapter Summary and Review 1068
Chapter Test 1079
Group Project 1080
viii CONTENTS
12
MORE ON SYSTEMS OF EQUATIONS 1083
12.1 Solving Systems of Equations in Two Variables 1084
12.2 Solving Systems of Equations in Three Variables 1103
12.3 Problem Solving Using Systems of Thee Equations 1114
12.4 Solving Systems of Equations Using Matrices 1122
12.5 Solving Systems of Equations Using Determinants 1134
Chapter Summary and Review 1145
Chapter Test 1154
Group Project 1155
Cumulative Review 1156
13
CONIC SECTIONS; MORE GRAPHING 1161
13.1 The Circle and the Parabola 1162
13.2 The Ellipse 1176
13.3 The Hyperbola 1186
13.4 Solving Nonlinear Systems of Equations 1197
Chapter Summary and Review 1205
Chapter Test 1210
Group Project 1212
14
MISCELLANEOUS TOPICS 1213
14.1 The Binomial Theorem 1214
14.2 Arithmetic Sequences and Series 1224
14.3 Geometric Sequences and Series 1235
Chapter Summary and Review 1248
Chapter Test 1252
Group Project 1253
Cumulative Review 1254
APPENDIXES APPENDIX 1: Roots and Powers A-1
APPENDIX 2: Synthetic Division A-2
APPENDIX 3: Answers to Selected Exercises A-9
INDEX I-1
PREFACE
Elementary and Intermediate Algebra, Fourth Edition, is more than a simple upgrade of the
third edition. Substantial changes have been made to the example structure, the Study Sets,
and the pedagogy. Throughout the process, the objective has been to ease teaching challenges
and meet students’educational needs.
Algebra, for many of today’s developmental math students, is like a foreign language.
They have difficulty translating the words, their meanings, and how they apply to problem
solving. With these needs in mind (and as educational research suggests), the fundamental
goal is to have students read, write, think, and speak using the language of algebra. Instruc-
tional approaches that include vocabulary, practice, and well-defined pedagogy, along with an
emphasis on reasoning, modeling, communication, and technology skills have been blended
to address this need.
The most common student question as they watch their instructors solve problems and as
they read the textbook is . . . Why?The new fourth edition addresses this question in a unique
way. Experience teaches us that it’s not enough to know how a problem is solved. Students
gain a deeper understanding of algebraic concepts if they know whya particular approach is
taken. This instructional truth was the motivation for adding aStrategyand Whyexplanation
to the solution of each worked example. The fourth edition now provides, on a consistent
basis, a concise answer to that all-important question: Why?
This is just one of several changes in this revision, and we trust that all of them will make
the course a better experience for both instructor and student.
NEW TO THIS EDITION
•
New Example Structure
•
New Chapter Opening Applications
•
New Study Skills Workshops
•
New Chapter Objectives
•
New Guided Practiceand Try It Yourselfsections in the Study Sets
•
New End-of-Chapter Organization
ix