College Algebra

College Algebra

James Stewart
McMaster University

Lothar Redlln
The Pennsylvania State University, Abington Campus

Saleem Watson
California State University.Long Beach

CONTENTS

P. Prerequisites 1
P.1 Modeling the Real World with Algebra 2
P.2 Real Numbers and Their Properties 7
P.3 The Real Number Line and Order 13
P.4 Integer Exponents 19
P.5 Rational Exponents and Radicals 26
P.6 Algebraic Expressions 32
DISCOVERY PROJECT Visualizing a Formula 38
P.7 Factoring 39
P.8 Rational Expressions 45
CHAPTER P Review 54
CHAPTER P Test 58
FOCUS ON PROBLEM SOLVING General Principles 59

1 Equations and Inequalities 65
1.1 Basic Equations 66
1.2 Modeling with Equations 74
DISCOVERY PROJECT Equations Through the Ages 86
1.3 Quadratic Equations 87
1.4 Complex Numbers 97
1.5 Other Types of Equations 103
1.6 Inequalities 112
1.7 Absolute Value Equations and Inequalities 121
CHAPTER 1 Review 125
CHAPTER 1 Test 129
FOCUS ON MODELING Making the Best Decisions 130

2 Coordinates and Graphs 137
2.1 The Coordinate Plane 138
DISCOVERY PROJECT Visualizing Data 145
2.2 Graphs of Equations in Two Variables 147
2.3 Graphing Calculators: Solving Equations and
Inequalities Graphically 156
2.4 Lines 166
2.5 Making Models Using Variation 179
CHAPTER 2 Review 185
CHAPTER 2 Test 189
CUMULATIVE REVIEW TEST: Chapters 1 and 2 190
FOCUS ON MODELING Fitting Lines to Data 192

3 Functions 203
3.1 What is a Function? 204
3.2 Graphs of Functions 214
DISCOVERY PROJECT Relations and Functions 225
3.3 Getting Information from the Graph of a Function 227
3.4 Average Rate of Change of a Function 236
3.5 Transformations of Functions 243
3.6 Combining Functions 254
DISCOVERY PROJECT Iteration and Chaos 263
3.7 One-to-One Functions and Their Inverses 265
CHAPTER 3 Review 273
CHAPTER 3 Test 278
FOCUS ON MODELING Modeling with Functions 280

4 Polynomial and Rational Functions 291
4.1 Quadratic Functions and Models 292
4.2 Polynomial Functions and Their Graphs 300
4.3 Dividing Polynomials 315
4.4 Real Zeros of Polynomials 321
DISCOVERY PROJECT Zeroing in on a Zero 333
4.5 Complex Zeros and the Fundamental Theorem of Algebra 335
4.6 Rational Functions 343
CHAPTER 4 Review 359
CHAPTER 4 Test 363
FOCUS ON MODELING Fitting Polynomial Curves
to Data 364

5 Exponential and Logarithmic Functions 369
5.1 Exponential Functions 370
DISCOVERY PROJECT Exponential Explosion 383
5.2 Logarithmic Functions 384
5.3 Laws of Logarithms 394
5.4 Exponential and Logarithmic Equations 400
5.5 Modeling with Exponential and Logarithmic Functions 411
CHAPTER 5 Review 423
CHAPTER 5 Test 428
CUMULATIVE REVIEW TEST: Chapters 3, 4, and 5 429
FOCUS ON MODELING Fitting Exponential and
Power Curves to Data 431

6 Systems of Equations and Inequalities 441
6.1 Systems of Equations 442
6.2 Systems of Linear Equations in Two Variables 450
6.3 Systems of Linear Equations in Several Variables 457
DISCOVERY PROJECT Best Fit Versus Exact Fit 467
6.4 Partial Fractions 469
6.5 Systems of Inequalities 474
CHAPTER 6 Review 481
CHAPTER 6 Test 485
FOCUS ON MODELING Linear Programming 486

7 Matrices and Determinants 493
7.1 Matrices and Systems of Linear Equations 494
7.2 The Algebra of Matrices 507
DISCOVERY PROJECT Will the Species Survive? 519
7.3 Inverses of Matrices and Matrix Equations 520
7.4 Determinants and Cramer’s Rule 530
CHAPTER 7 Review 541
CHAPTER 7 Test 546
FOCUS ON MODELING Computer Graphics 547

8 Conic Sections 551
8.1 Parabolas 552
DISCOVERY PROJECT Rolling Down a Ramp 562
8.2 Ellipses 563
8.3 Hyperbolas 572
8.4 Shifted Conics 581
CHAPTER 8 Review 589
CHAPTER 8 Test 592
CUMULATIVE REVIEW TEST: Chapters 6, 7, and 8 593
FOCUS ON MODELING Conics in Architecture 595

9 Sequences and Series 599
9.1 Sequences and Summation Notation 600
9.2 Arithmetic Sequences 610
9.3 Geometric Sequences 616
DISCOVERY PROJECT Finding Patterns 625
9.4 Mathematics of Finance 626
9.5 Mathematical Induction 632
9.6 The Binomial Theorem 638
CHAPTER 9 Review 647
CHAPTER 9 Test 651
FOCUS ON MODELING Modeling with Recursive
Sequences 652

10 Counting and Probability 657
10.1 Counting Principles 658
10.2 Permutations and Combinations 662
10.3 Probability 672
DISCOVERY PROJECT Small Samples, Big Results 684
10.4 Binomial Probability 685
10.5 Expected Value 690
CHAPTER 10 Review 692
CHAPTER 10 Test 696
CUMULATIVE REVIEW TEST: Chapters 9 and 10 697
FOCUS ON MODELING The Monte Carlo Method 699

ANSWERS A1
INDEX I1
PHOTO CREDITS P1