Table of Contents
How to Use This Book vii
Study Unit I Algebra and Graphing Methods
1 Basic Algebraic Methods 3
Lesson 1-1 Real Numbers, Variables, and Exponents 3
Lesson 1-2 Solving Linear Equations 6
Lesson 1-3 Solving Linear Inequalities 10
Lesson 1-4 Operations with Polynomials 15
Lesson 1-5 Factoring Polynomials 19
Lesson 1-6 Factoring Quadratic Trinomials 22
Lesson 1-7 Special Products and Factoring Patterns 24
Review Exercises 27
2 Rational and Irrational Expressions 31
Lesson 2-1 Operations with Rational Expressions 31
Lesson 2-2 Simplifying Complex Fractions 37
Lesson 2-3 Radicals and Fractional Exponents 39
Lesson 2-4 Operations with Radicals 41
Review Exercises 46
3 Graphing and Systems of Equations 51
Lesson 3-1 Graphing Points and Linear Equations 52
Lesson 3-2 Midpoint and Distance Formulas 53
Lesson 3-3 The Slope of a Line 56
Lesson 3-4 Graphing a Linear Equation 58
Lesson 3-5 Graphing a Linear Inequality 59
Lesson 3-6 Writing Equations of Lines 61
Lesson 3-7 Solving Linear Systems Graphically 68
Lesson 3-8 Solving Linear Systems Algebraically 72
Review Exercises 76
4 Functions and Quadratic Equations 81
Lesson 4-1 Function Concepts 82
Lesson 4-2 Quadratic Functions and Their Graphs 89
Lesson 4-3 Solving Quadratic Equations 92
Lesson 4-4 Solving a Linear-Quadratic System 97
Lesson 4-5 Applying Quadratic Equations 99
Lesson 4-6 Solving Quadratic Inequalities 102
Review Exercises 105
5 Complex Numbers and the Quadratic Formula 111
Lesson 5-1 Complex Numbers 111
Lesson 5-2 Multiplying and Dividing Complex Numbers 114
Lesson 5-3 Completing the Square 115
Lesson 5-4 The Quadratic Formula 117
Review Exercises 122
Study Unit II Functions and their Graphs
6 Special Functions and Equations 129
Lesson 6-1 Absolute-Value Equations and Inequalities 129
Lesson 6-2 Transformations of Graphs 134
Lesson 6-3 Special Functions and Their Graphs 138
Lesson 6-4 Radical Equations 142
Lesson 6-5 Rational Equations and Inequalities 144
Review Exercises 149
7 Polynomial and Rational Functions 155
Lesson 7-1 Division of Polynomials 156
Lesson 7-2 Zeros of Polynomial Functions 165
Lesson 7-3 Solving Polynomial Equations 176
Lesson 7-4 Graphing Polynomial Functions 181
Lesson 7-5 Graphing Rational Functions 191
Lesson 7-6 Decomposing Rational Expressions 198
Review Exercises 203
8 Exponential and Logarithmic Functions 207
Lesson 8-1 Inverse Functions 207
Lesson 8-2 The Exponential Function 217
Lesson 8-3 The Logarithmic Function 219
Lesson 8-4 Logarithm Laws and Equations 223
Lesson 8-5 Exponential and Logarithmic Models 229
Review Exercises 237
Study Unit III Trigonometric Analysis
9 Trigonometry 247
Lesson 9-1 Degree and Radian Measures 248
Lesson 9-2 Right-Triangle Trigonometry 250
Lesson 9-3 The General Angle 254
Lesson 9-4 Working with Trigonometric Functions 258
Lesson 9-5 Trigonometric Functions of Special Angles 261
Review Exercises 264
10 Graphing Trigonometric Functions 271
Lesson 10-1 Periodic Functions and Their Graphs 271
Lesson 10-2 Graphing Trigonometric Functions 277
Lesson 10-3 Transformations of Trigonometric Functions 283
Lesson 10-4 Inverse Trigonometric Functions 286
Review Exercises 289
11 Trigonometric Identities and Equations 297
Lesson 11-1 Pythagorean Trigonometric Identities 297
Lesson 11-2 Solving Trigonometric Equations 301
Lesson 11-3 Sum and Difference Identities 303
Lesson 11-4 Double-Angle Identities 306
Lesson 11-5 Half-Angle Identities 308
Review Exercises 310
12 Solving Triangles 315
Lesson 12-1 The Area of a Triangle 315
Lesson 12-2 The Law of Sines 317
Lesson 12-3 The Law of Cosines 323
Review Exercises 326
Study Unit IV Polar Coordinates and Conic Sections
13 Polar Coordinates and Parametric Equations 337
Lesson 13-1 Parametric Equations 338
Lesson 13-2 The Polar Coordinate System 341
Lesson 13-3 The Polar Form of a Complex Number 350
Lesson 13-4 Powers and Roots of Complex Numbers 354
Review Exercises 359
14 Conic Sections and their Equations 363
Lesson 14-1 The Parabola 364
Lesson 14-2 The Ellipse 372
Lesson 14-3 The Hyperbola 380
Lesson 14-4 General Equations of Conics 388
Lesson 14-5 Polar Equations of Conics 396
Review Exercises 400
Study Unit V Number Patterns and Calculus PREVIEW
15 Sequences, Series, and Counting 407
Lesson 15-1 Arithmetic Sequences and Series 408
Lesson 15-2 Geometric Sequences and Series 412
Lesson 15-3 Generalized Sequences 414
Lesson 15-4 Mathematical Induction 418
Lesson 15-5 Permutations and Combinations 422
Lesson 15-6 The Binomial Theorem 424
Review Exercises 427
16 Calculus Preview 433
Lesson 16-1 Limits of Functions 433
Lesson 16-2 Slope of a Tangent Line 446
Lesson 16-3 Rules for Finding Derivatives 451
Lesson 16-4 Finding Antiderivatives 454
Lesson 16-5 Integration and Area Under a Curve 457
Review Exercises 461
Appendix: Graphing with a Calculator 465
Answers to Chapter Review Exercises 469
Index 507