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Chapter 1
Basic Algebra
1.1 Real Numbers 2
1.2 Algebraic Expressions and Geometric Formulas 16
1.3 Integer Exponents 24
1.4 Products of Algebraic Expressions 34
1.5 Linear Equations and Literal Equations 41
1.6 Applications of Linear Equations 49
1.7 Linear Inequalities in One Variable 59
1.8 Compound Inequalities 65
Chapter 1 Overview 71
Chapter 1 Review Exercises 72
Chapter 1 Test 74
Chapter 2
Functions and Graphs
2.1 Functions, Relations, and Ordered Pairs 76
2.2 Functions and Graphs 84
2.3 Variation 98
2.4 Functional Notation and Piecewise Functions 104
2.5 Graphing Techniques 112
2.6 Absolute Value Equations and Inequalities 119
2.7 The Slope of a Line and the Distance Formula 128
2.8 Linear Functions 136
Chapter 2 Overview 145
Chapter 2 Review Exercises 146
Chapter 2 Test 149
Chapter 3
Systems of Linear Equations
3.1 Systems of Linear Equations in Two Variables 152
3.2 Systems of Linear Equations in Three Variables 165
3.3 Triangular Form and Matrices 173
3.4 Determinants and Cramer’s Rule 180
Chapter 3 Overview 190
Chapter 3 Review Exercises 191
Chapter 3 Test 192
Chapter 4
Introduction to Trigonometry
4.1 Trigonometric Functions of Acute Angles 196
4.2 Right Triangle Applications 207
4.3 Trigonometric Functions of General Angles 213
4.4 Introduction to Trigonometric Equations 223
4.5 Vectors 231
Chapter 4 Overview 237
Chapter 4 Review Exercises 238
Chapter 4 Test 240
Chapter 5
Further Algebraic Techniques
5.1 Factoring Polynomial and Trigonometric
Expressions 242
5.2 Special Factoring Models and a Factoring Strategy 251
5.3 Solving Equations by Factoring 259
5.4 Multiplication and Division of Fractions 268
5.5 Addition and Subtraction of Fractions 276
5.6 Complex Fractions 286
5.7 Division of Polynomials 293
5.8 Equations That Contain Fractions 299
Chapter 5 Overview 309
Chapter 5 Review Exercises 310
Chapter 5 Test 312
Chapter 6
Radicals and Complex Numbers
6.1 Radicals and Rational Exponents 314
6.2 Product and Quotient Properties of Radicals 321
6.3 Addition and Subtraction of Radicals 328
6.4 Further Radical Simplification 334
6.5 Radical Equations 340
6.6 Complex Numbers 345
6.7 Trigonometric Form of Complex Numbers 353
Chapter 6 Overview 360
Chapter 6 Review Exercises 361
Chapter 6 Test 363
Chapter 7
Second-Degree Equations in One and Two Variables
7.1 Solving Quadratic Equations by Completing
the Square 366
7.2 The Quadratic Formula 373
7.3 Other Equations Which Lead to Quadratic
Equations 380
7.4 Solving Inequalities Involving Polynomials 385
7.5 Quadratic Functions and Parabolas 393
7.6 The Circle 403
7.7 The Ellipse and the Hyperbola 408
7.8 Nonlinear Systems of Equations 414
Chapter 7 Overview 419
Chapter 7 Review Exercises 420
Chapter 7 Test 422
Chapter 8
Exponential and Logarithmic Functions
8.1 Exponential Functions 424
8.2 Inverse Functions 432
8.3 Logarithmic Functions 440
8.4 Properties of Logarithms 448
8.5 Exponential and Logarithmic Equations 454
8.6 More Applications and the Number e 460Chapter 8 Overview 468
Chapter 8 Review Exercises 469
Chapter 8 Test 471
Chapter 9
Topics in Trigonometry
9.1 Radians 474
9.2 Trigonometric Functions of Real Numbers 480
9.3 Graphs of Sine and Cosine Functions 490
9.4 Other Trigonometric Graphs and Fundamental
Identities 500
9.5 Inverse Trigonometric Functions 509
9.6 Trigonometric Equations 517
9.7 Law of Sines 523
9.8 Law of Cosines and Area of Triangles 531Chapter 9 Overview 539
Chapter 9 Review Exercises 541
Chapter 9 Test 543
Chapter 10
Sequences, Series, and the Binomial Theorem
10.1 Sequences 546
10.2 Series 554
10.3 Infinite Geometric Series 562
10.4 Binomial Theorem 566Chapter 10 Overview 573
Chapter 10 Review Exercises 574
Chapter 10 Test 575
Chapter 11
Polynomial and Rational Functions
11.1 Zeros and Graphs of Polynomial Functions 578
11.2 Synthetic Division and Theorems About Zeros 587
11.3 Additional Theorems About Zeros 598
11.4 Rational Functions 606Chapter 11 Overview 616
Chapter 11 Review Exercises 616
Chapter 11 Test 617
Answers to Progress Check Exercises A-1
Answers to Odd-Numbered Problems A-15
Index I-1
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