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Foundations: A Prelude to Functions | |

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The Distance and Midpoint Formulas | |

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Graphs of Equations in Two Variables; Intercepts; Symmetry | |

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Lines | |

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Circles | |

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Functions and Their Graphs | |

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Functions | |

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The Graph of a Function | |

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Properties of Functions | |

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Library of Functions; Piecewise-defined Functions | |

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Graphing Techniques: Transformations | |

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Mathematical Models: Constructing Functions | |

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Building Mathematical Models Using Variation | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Linear and Quadratic Functions | |

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Properties of Linear Functions and Linear Models | |

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Building Linear Models from Data | |

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Quadratic Functions and Their Zeros | |

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Properties of Quadratic Functions | |

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Inequalities Involving Quadratic Functions | |

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Building Quadratic Models from Verbal Descriptions and from Data | |

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Complex Zeros of a Quadratic Function | |

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Equations and Inequalities Involving the Absolute Value Function | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Polynomial and Rational Functions | |

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Polynomial Functions and Models | |

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Properties of Rational Functions | |

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The Graph of a Rational Function | |

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Polynomial and Rational Inequalities | |

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The Real Zeros of a Polynomial Function | |

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Complex Zeros; Fundamental Theorem of Algebra | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Exponential and Logarithmic Functions | |

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Composite Functions | |

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One-to-One Functions; Inverse Functions | |

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Exponential Functions | |

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Logarithmic Functions | |

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Properties of Logarithms | |

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Logarithmic and Exponential Equations | |

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Compound Interest | |

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Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay | |

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Building Exponential, Logarithmic, and Logistic Functions from Data | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Trigonometric Functions | |

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Angles and Their Measure | |

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Trigonometric Functions: Unit Circle Approach | |

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Properties of the Trigonometric Functions | |

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Graphs of the Sine and Cosine Functions | |

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Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions | |

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Phase Shift; Sinusoidal Curve Fitting | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Analytic Trigonometry | |

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The Inverse Sine, Cosine, and Tangent Functions | |

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The Inverse Trigonometric Functions (Continued) | |

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Trigonometric Identities | |

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Sum and Difference Formulas | |

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Double-angle and Half-angle Formulas | |

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Product-to-Sum and Sum-to-Product Formulas | |

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Trigonometric Equations | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Applications of Trigonometric Functions | |

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Applications Involving Right Triangles | |

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The Law of Sines | |

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The Law of Cosines | |

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Area of a Triangle | |

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Simple Harmonic Motion; Damped Motion; Combining Waves | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Polar Coordinates; Vectors | |

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Polar Coordinates | |

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Polar Equations and Graphs | |

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The Complex Plane; DeMoivre's Theorem | |

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Vectors | |

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The Dot Product | |

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Vectors in Space | |

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The Cross Product | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Analytic Geometry | |

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Conics | |

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The Parabola | |

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The Ellipse | |

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The Hyperbola | |

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Rotation of Axes; General Form of a Conic | |

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Polar Equations of Conics | |

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Plane Curves and Parametric Equations | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Systems of Equations and Inequalities | |

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Systems of Linear Equations: Substitution and Elimination | |

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Systems of Linear Equations: Matrices | |

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Systems of Linear Equations: Determinants | |

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Matrix Algebra | |

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Partial Fraction Decomposition | |

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Systems of Nonlinear Equations | |

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Systems of Inequalities | |

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Linear Programming | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Sequences; Induction; the Binomial Theorem | |

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Sequences | |

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Arithmetic Sequences | |

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Geometric Sequences; Geometric Series | |

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Mathematical Induction | |

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The Binomial Theorem | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Counting and Probability | |

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Counting | |

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Permutations and Combinations | |

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Probability | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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A Preview of Calculus: the Limit; Derivative, and Integral of a Function | |

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Finding Limits Using Tables and Graphs | |

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Algebra Techniques for Finding Limits | |

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One-sided Limits; Continuous Functions | |

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The Tangent Problem; the Derivative | |

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The Area Problem; the Integral | |

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Chapter Review | |

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Chapter Test | |

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Chapter Projects | |

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Cumulative Review | |

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Review | |

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Algebra Essentials | |

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Geometry Essentials | |

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Polynomials | |

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Factoring Polynomials | |

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Synthetic Division | |

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Rational Expressions | |

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Nth Roots; Rational Exponents | |

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Solving Equations | |

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Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs | |

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Interval Notation; Solving Inequalities | |

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Complex Numbers | |

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Graphing Utilities | |

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The Viewing Rectangle | |

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Using a Graphing Utility to Graph Equations | |

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Using a Graphing Utility to Locate Intercepts and Check for Symmetry | |

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Using a Graphing Utility to Solve Equations | |

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Square Screens | |

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Using a Graphing Utility to Graph Inequalities | |

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Using a Graphing Utility to Solve Systems of Linear Equations | |

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Using a Graphing Utility to Graph a Polar Equation | |

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Using a Graphing Utility to Graph Parametric Equations | |

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Answers | |

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Index | |