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Table of Contents:
1. Graphs 1.1 The Distance and Midpoint Formulas 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 1.3 Lines 1.4 Circles   2. Functions and Their Graphs 2.1 Functions 2.2 The Graph of a Function 2.3 Properties of Functions 2.4 Library of Functions; Piecewise-defined Functions 2.5 Graphing Techniques: Transformations 2.6 Mathematical Models: Building Functions   3. Linear and Quadratic Functions 3.1 Properties of Linear Functions and Linear Models 3.2 Building Linear Models from Data 3.3 Quadratic Functions and Their Properties 3.4 Build Quadratic Models from Verbal Descriptions and from Data 3.5 Inequalities Involving Quadratic Functions   4. Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Properties of Rational Functions 4.3 The Graph of a Rational Function 4.4 Polynomial and Rational Inequalities 4.5 The Real Zeros of a Polynomial Function 4.6 Complex Zeros; Fundamental Theorem of Algebra   5. Exponential and Logarithmic Functions 5.1 Composite Functions 5.2 One-to-One Functions; Inverse Functions 5.3 Exponential Functions 5.4 Logarithmic Functions 5.5 Properties of Logarithms 5.6 Logarithmic and Exponential Equations 5.7 Financial Models 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 5.9 Building Exponential, Logarithmic, and Logistic Models from Data   6. Trigonometric Functions 6.1 Angles and Their Measure 6.2 Trigonometric Functions: Unit Circle Approach 6.3 Properties of the Trigonometric Functions 6.4 Graphs of the Sine and Cosine Functions 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 6.6 Phase Shift; Sinusoidal Curve Fitting   7. Analytic Trigonometry 7.1 The Inverse Sine, Cosine, and Tangent Functions 7.2 The Inverse Trigonometric Functions (Continued) 7.3 Trigonometric Equations 7.4 Trigonometric Identities 7.5 Sum and Difference Formulas 7.6 Double-angle and Half-angle Formulas 7.7 Product-to-Sum and Sum-to-Product Formulas   8. Applications of Trigonometric Functions 8.1 Right Triangle Trigonometry; Applications 8.2 The Law of Sines 8.3 The Law of Cosines 8.4 Area of a Triangle 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves   9. Polar Coordinates; Vectors 9.1 Polar Coordinates 9.2 Polar Equations and Graphs 9.3 The Complex Plane; DeMoivre’s Theorem 9.4 Vectors 9.5 The Dot Product 9.6 Vectors in Space 9.7 The Cross Product   10. Analytic Geometry 10.1 Conics 10.2 The Parabola 10.3 The Ellipse 10.4 The Hyperbola 10.5 Rotation of Axes; General Form of a Conic 10.6 Polar Equations of Conics 10.7 Plane Curves and Parametric Equations   11. Systems of Equations and Inequalities 11.1 Systems of Linear Equations: Substitution and Elimination 11.2 Systems of Linear Equations: Matrices 11.3 Systems of Linear Equations: Determinants 11.4 Matrix Algebra 11.5 Partial Fraction Decomposition 11.6 Systems of Nonlinear Equations 11.7 Systems of Inequalities 11.8 Linear Programming   12. Sequences; Induction; the Binomial Theorem 12.1 Sequences 12.2 Arithmetic Sequences 12.3 Geometric Sequences; Geometric Series 12.4 Mathematical Induction 12.5 The Binomial Theorem   13. Counting and Probability 13.1 Counting 13.2 Permutations and Combinations 13.3 Probability   14. A Preview of Calculus: The Limit, Derivative, and Integral of a Function 14.1 Finding Limits Using Tables and Graphs 14.2 Algebra Techniques for Finding Limits 14.3 One-sided Limits; Continuous Functions 14.4 The Tangent Problem; The Derivative 14.5 The Area Problem; The Integral   Appendix A: Review A.1 Algebra Essentials A.2 Geometry Essentials A.3 Polynomials A.4 Synthetic Division A.5 Rational Expressions A.6 Solving Equations A.7 Complex Numbers; Quadratic Equations in the Complex Number System A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications A.9 Interval Notation; Solving Inequalities A.10 nth Roots; Rational Exponents   Appendix B: Graphing Utilities B.1 The Viewing Rectangle B.2 Using a Graphing Utility to Graph Equations B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry B.4 Using a Graphing Utility to Solve Equations B.5 Square Screens B.6 Using a Graphing Utility to Graph Inequalities B.7 Using a Graphing Utility to Solve Systems of Linear Equations B.8 Using a Graphing Utility to Graph a Polar Equation B.9 Using a Graphing Utility to Graph Parametric Equations