| |
| |
| Preface | |
| |
| |
| To the Student | |
| |
| |
| Are You Ready for College Algebra? | |
| |
| |
| Prologue: Principles of Problem Solving | |
| |
| |
| |
| Prerequisites | |
| |
| |
| Modeling the Real World with Algebra | |
| |
| |
| The Real Numbers | |
| |
| |
| Integer Exponents and Scientific Notation | |
| |
| |
| Rational Exponents and Radicals | |
| |
| |
| Algebraic Expressions | |
| |
| |
| Factoring | |
| |
| |
| Rational Expressions | |
| |
| |
| Solving Basic Equations | |
| |
| |
| Chapter P Review | |
| |
| |
| Chapter P Test | |
| |
| |
| FOCUS ON MODELING: Making the Best Decisions | |
| |
| |
| |
| Equations and Graphs | |
| |
| |
| The Coordinate Plane | |
| |
| |
| Graphs of Equations in Two Variables; Circles | |
| |
| |
| Lines | |
| |
| |
| Solving Equations Graphically | |
| |
| |
| Modeling with Equations | |
| |
| |
| Solving Quadratic Equations | |
| |
| |
| Solving Other Types of Equations | |
| |
| |
| Solving Inequalities | |
| |
| |
| Solving Absolute Value Equations and Inequalities | |
| |
| |
| Chapter 1 Review | |
| |
| |
| Chapter 1 Test | |
| |
| |
| FOCUS ON MODELING: Fitting Lines to Data | |
| |
| |
| |
| Functions | |
| |
| |
| Functions | |
| |
| |
| Graphs of Functions | |
| |
| |
| Getting Information from the Graph of a Function | |
| |
| |
| Average Rate of Change of a Function | |
| |
| |
| Transformations of Functions | |
| |
| |
| Combining Functions | |
| |
| |
| One-to-One Functions and Their Inverses | |
| |
| |
| Chapter 2 Review | |
| |
| |
| Chapter 2 Test | |
| |
| |
| FOCUS ON MODELING: Modeling with Functions | |
| |
| |
| |
| Polynomial and Rational Function | |
| |
| |
| Quadratic Functions and Models | |
| |
| |
| Polynomial Functions and Their Graphs | |
| |
| |
| Dividing Polynomials | |
| |
| |
| Real Zeros of Polynomials | |
| |
| |
| Complex Numbers | |
| |
| |
| Complex Zeros and the Fundamental Theorem of Algebra | |
| |
| |
| Rational Functions | |
| |
| |
| Modeling Variation | |
| |
| |
| Chapter 3 Review | |
| |
| |
| Chapter 3 Test | |
| |
| |
| FOCUS ON MODELING: Fitting Polynomial Curves to Data | |
| |
| |
| |
| Exponential and Logarithmic Functions | |
| |
| |
| Exponential Functions | |
| |
| |
| The Natural Exponential Function | |
| |
| |
| Logarithmic Functions | |
| |
| |
| Laws of Logarithms | |
| |
| |
| Exponential and Logarithmic Equations | |
| |
| |
| Modeling with Exponential and Logarithmic Functions | |
| |
| |
| Chapter 4 Review | |
| |
| |
| Chapter 4 Test | |
| |
| |
| Cumulative Review Test: Chapters 2, 3, and 4 | |
| |
| |
| FOCUS ON MODELING: Fitting Exponential and Power Curves to Data | |
| |
| |
| |
| Systems of Equations and Inequalities | |
| |
| |
| Systems of Linear Equations in Two Variables | |
| |
| |
| Systems of Linear Equations in Several Variables | |
| |
| |
| Partial Fractions | |
| |
| |
| Systems of Nonlinear Equations | |
| |
| |
| Systems of Inequalities | |
| |
| |
| Chapter 5 Review | |
| |
| |
| Chapter 5 Test | |
| |
| |
| FOCUS ON MODELING: Linear Programming | |
| |
| |
| |
| Matrices and Determinants | |
| |
| |
| Matrices and Systems of Linear Equations | |
| |
| |
| The Algebra of Matrices | |
| |
| |
| Inverses of Matrices and Matrix Equations | |
| |
| |
| Determinants and Cramer's Rules | |
| |
| |
| Chapter 6 Review | |
| |
| |
| Chapter 6 Test | |
| |
| |
| FOCUS ON MODELING: Computer Graphics | |
| |
| |
| |
| Conic Sections | |
| |
| |
| Parabolas | |
| |
| |
| Ellipses | |
| |
| |
| Hyperbolas | |
| |
| |
| Shifted Conics | |
| |
| |
| Chapter 7 Review | |
| |
| |
| Chapter 7 Test | |
| |
| |
| Cumulative Review Test: Chapters 5, 6, and 7 | |
| |
| |
| FOCUS ON MODELING: Conics in Architecture | |
| |
| |
| |
| Sequences and Series | |
| |
| |
| Sequences and Summation Notation | |
| |
| |
| Arithmetic Sequences | |
| |
| |
| Geometric Sequences | |
| |
| |
| Mathematics of Finance | |
| |
| |
| Mathematical Induction | |
| |
| |
| The Binomial Theorem | |
| |
| |
| Chapter 8 Review | |
| |
| |
| Chapter 8 Test | |
| |
| |
| FOCUS ON MODELING: Modeling with Recursive Sequences | |
| |
| |
| |
| Probability and Statistics | |
| |
| |
| Counting | |
| |
| |
| Probability | |
| |
| |
| Binomial Probability | |
| |
| |
| Expected Value | |
| |
| |
| Chapter 9 Review | |
| |
| |
| Chapter 9 Test | |
| |
| |
| Cumulative Review Test: Chapters 8 and 9 | |
| |
| |
| FOCUS ON MODELING: The Monte Carlo Method | |
| |
| |
| |
| Calculations and Calculations | |
| |
| |
| |
| Graphing with a Graphing Calculator | |
| |
| |
| |
| Using the TI-83/84 Graphing Calculator | |