Table of Contents
Introduction xiii
Chapter 1 Fundamentals 1
The Distributive Property 2
Rational Expressions 7
Simplifying Rational Expressions 8
Multiplying Rational Expressions 8
Adding Rational Expressions 9
Exponents and Roots 13
Summary 17
Quiz 18
Chapter 2 Linear Equations and Inequalities 21
Basic Linear Equations 22
Equations Leading to Linear Equations 25
Absolute Value Equations 30
Linear Inequalities 35
Compound Inequalities 36
Absolute Value Inequalities 39
Summary 47
Quiz 49
Chapter 3 Quadratic Equations 51
Solving Quadratic Equations by Factoring 52
The Quadratic Formula 53
Completing the Square 56
Summary 63
Quiz 64
Chapter 4 The xy-Coordinate Plane 65
Plotting Points 66
The Distance Between Two Points 67
The Midpoint Formula 76
Circles 77
Summary 88
Quiz 89
Chapter 5 Lines and Parabolas 91
Introduction to Lines 92
Intercepts 95
The Slope of a Line 102
Horizontal and Vertical Lines 105
Finding an Equation for a Line 107
The Slope-Intercept Form of a Line 112
Graphing the Line Using the Slope and y-Intercept 113
Parallel and Perpendicular Lines 116
Linear Applications 123
Parabolas 134
Sketching the Graph of a Parabola 135
Locating the Vertex by Completing the Square 141
Summary 147
Quiz 149
Chapter 6 Nonlinear Inequalities 153
Solving Nonlinear Inequalities Graphically 154
Solving Nonlinear Inequalities 157
Sign Graphs 159
Rational Inequalities 165
Summary 173
Quiz 174
Chapter 7 Functions 175
Introduction to Functions 176
Evaluating Functions 178
Evaluating Piecewise Functions 180
Domain and Range 182
Functions and Their Graphs 188
Finding the Domain and Range Graphically 193
Increasing Intervals and Decreasing Intervals 197
The Graph of a Piecewise Function 200
More on Evaluating Functions 209
The Difference Quotient 212
Summary 217
Quiz 220
Chapter 8 Quadratic Functions 223
A Review of a Parabola's Vertex 224
The Range of a Quadratic Function 226
The Maximum/Minimum of a Quadratic Function 228
Applied Maximum/Minimum Problems 230
Revenue-Maximizing Price 239
Maximizing/Minimizing Other Functions 242
Summary 243
Quiz 244
Chapter 9 Transformations and Combinations 247
Transformations 248
Reflections, and Vertical Stretching and Compressing 253
Sketching the Graph of a Transformation 259
Special Functions 264
Even/Odd Functions 281
Combining Functions 286
Function Composition 287
Function Composition for a Single Value 290
The Domain for the Composition of Functions 295
Summary 298
Quiz 300
Chapter 10 Polynomial Functions 305
Introduction to Polynomial Functions 306
Sketching Graphs of Polynomials 314
Polynomial Division 317
Synthetic Division 324
Synthetic Division and Factoring 331
Rule of Signs and Upper and Lower Bounds Theorem 340
Complex Numbers 346
Complex Solutions to Quadratic Equations 354
The Fundamental Theorem of Algebra 357
Summary 370
Quiz 372
Chapter 11 Systems of Equations and Inequalities 375
Systems of Linear Equations 376
Elimination by Addition 380
Applications for Systems of Equations 390
Systems Containing Nonlinear Equations 396
Inequalities and Systems of Inequalities 401
Systems of Inequalities 408
Summary 419
Quiz 421
Chapter 12 Exponents and Logarithms 425
Compound Growth 426
The Number e 430
Increasing Population 431
Logarithms 434
Properties of Logarithms 436
Three More Important Logarithm Properties 439
Using Multiple Logarithm Properties 441
Equations Involving Exponents and Logarithms 445
Exponent and Logarithm Functions 453
The Domain of a Logarithm Function 459
Summary 460
Quiz 463
Final Exam 467
Answers to Quizzes and Final Exam 483
Index 487
