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| Preface | |
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| To the Student | |
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| Calculators and Calculations | |
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| Prerequisites | |
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| Chapter Overview | |
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| Modeling the Real World | |
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| Real Numbers | |
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| Integer Exponents | |
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| Rational Exponents and Radicals | |
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| Algebraic Expressions | |
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| Discovery Project: Visualizing a Formula | |
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| Factoring | |
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| Rational Expressions | |
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| Chapter P Review | |
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| Chapter P Test | |
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| Focus on Problem Solving: General Principles | |
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| Equations and Inequalities | |
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| Chapter Overview | |
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| Basic Equations | |
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| Modeling with Equations | |
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| Discovery Project: Equations through the Ages | |
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| Quadratic Equations | |
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| Complex Numbers | |
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| Other Types of Equations | |
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| Inequalities | |
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| Absolute Value Equations and Inequalities | |
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| Chapter 1 Review | |
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| Chapter 1 Test | |
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| Focus on Modeling: Making the Best Decisions | |
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| Coordinates and Graphs | |
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| Chapter Overview | |
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| The Coordinate Plane | |
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| Discovery Project: Visualizing Data | |
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| Graphs of Equations in Two Variables | |
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| Graphing Calculators; Solving Equations and Inequalitie Graphically | |
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| Lines | |
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| Modeling: Variation | |
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| Chapter 2 Review | |
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| Chapter 2 Test | |
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| Focus on Modeling: Fitting Lines to Data | |
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| Functions | |
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| Chapter Overview | |
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| What Is a Function? | |
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| Graphs of Functions | |
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| Increasing and Decreasing Functions; Average Rate of Change | |
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| Transformations of Functions | |
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| Quadratic Functions; Maxima and Minima | |
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| Combining Functions | |
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| Discovery Project: Iteration and Chaos | |
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| One-to-One Functions and Their Inverses | |
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| Chapter 3 Review | |
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| Chapter 3 Test | |
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| Focus on Modeling: Modeling with Functions | |
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| Polynomial and Rational Functions | |
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| Chapter Overview | |
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| Polynomial Functions and Their Graphs | |
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| Dividing Polynomials | |
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| Real Zeros of Polynomials | |
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| Discovery Project: Zeroing in on a Zero | |
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| Complex Zeros and the Fundamental Theorem of Algebra | |
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| Rational Functions | |
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| Chapter 4 Review | |
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| Chapter 4 Test | |
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| Focus on Modeling: Fitting Polynomial Curves to Data | |
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| Exponential and Logarithmic Functions | |
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| Chapter Overview | |
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| Exponential Functions | |
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| Discovery Project: Exponential Explosion | |
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| Logarithmic Functions | |
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| Laws of Logarithms | |
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| Exponential and Logarithmic Equations | |
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| Modeling with Exponential and Logarithmic Functions | |
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| Chapter 5 Review | |
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| Chapter 5 Test | |
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| Focus on Modeling: Fitting Exponential and Power Curves to Data | |
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| Systems of Equations and Inequalities | |
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| Chapter Overview | |
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| Systems of Equations | |
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| Systems of Linear Equations in Two Variables | |
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| Systems of Linear Equations in Several Variables | |
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| Discovery Project: Exact Fit versus Best Fit | |
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| Systems of Inequalities | |
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| Partial Fractions | |
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| Chapter 6 Review | |
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| Chapter 6 Test | |
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| Focus on Modeling: Linear Programming | |
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| Matrices and Determinants | |
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| Chapter Overview | |
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| Matrices and Systems of Linear Equations | |
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| The Algebra of Matrices | |
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| Discovery Project: Will the Species Survive? | |
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| Inverses of Matrices and Matrix Equations | |
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| Determinants and Cramer's Rule | |
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| Chapter 7 Review | |
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| Chapter 7 Test | |
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| Focus on Modeling: Computer Graphics | |
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| Conic Sections | |
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| Chapter Overview | |
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| Parabolas | |
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| Discovery Project: Rolling Down a Ramp | |
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| Ellipses | |
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| Hyperbolas | |
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| Shifted Conics | |
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| Chapter 8 Review | |
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| Chapter 8 Test | |
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| Focus on Modeling: Conics in Architecture | |
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| Sequences and Series | |
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| Chapter Overview | |
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| Sequences and Summation Notation | |
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| Arithmetic Sequences | |
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| Geometric Sequences | |
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| Discovery Project: Finding Patterns | |
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| Mathematics of Finance | |
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| Mathematical Induction | |
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| The Binomial Theorem | |
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| Chapter 9 Review | |
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| Chapter 9 Test | |
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| Focus on Modeling: Modeling with Recursive Sequences | |
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| Counting and Probability | |
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| Chapter Overview | |
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| Counting Principles | |
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| Permutations and Combinations | |
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| Probability | |
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| Discovery Project: Small Samples, Big Results | |
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| Binomial Probability | |
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| Expected Value | |
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| Chapter 10 Review | |
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| Chapter 10 Test | |
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| Focus on Modeling: The Monte Carlo Method | |
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| Answers | |
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| Index | |
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| Photo Credits | |