Foundations: A Prelude to FunctionsF.1 The Distance and Midpoint FormulasF.2 Graphs of Equations in Two Variables; Intercepts; SymmetryF.3 LinesF.4 Circles 1. Functions and Their Graphs1.1 Functions1.2 The Graph of a Function1.3 Properties of Functions1.4 Library of Functions; Piecewise-defined Functions1.5 Graphing Techniques: Transformations1.6 Mathematical Models: Constructing Functions1.7 Building Mathematical Models Using Variation Chapter Review Chapter Test Chapter Projects 2. Linear and Quadratic Functions2.1 Properties of Linear Functions and Linear Models2.2 Building Linear Models from Data2.3 Quadratic Functions and Their Zeros2.4 Properties of Quadratic Functions2.5 Inequalities Involving Quadratic Functions2.6 Building Quadratic Models from Verbal Descriptions and from Data2.7 Complex Zeros of a Quadratic Function2.8 Equations and Inequalities Involving the Absolute Value Function Chapter Review Chapter Test Chapter Projects Cumulative Review 3. Polynomial and Rational Functions3.1 Polynomial Functions and Models3.2 Properties of Rational Functions3.3 The Graph of a Rational Function3.4 Polynomial and Rational Inequalities3.5 The Real Zeros of a Polynomial Function3.6 Complex Zeros; Fundamental Theorem of Algebra Chapter Review Chapter Test Chapter Projects Cumulative Review 4. Exponential and Logarithmic Functions4.1 Composite Functions4.2 One-to-One Functions; Inverse Functions4.3 Exponential Functions4.4 Logarithmic Functions4.5 Properties of Logarithms4.6 Logarithmic and Exponential Equations4.7 Compound Interest4.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay4.9 Building Exponential, Logarithmic, and Logistic Functions from Data Chapter Review Chapter Test Chapter Projects Cumulative Review 5. Trigonometric Functions5.1 Angles and Their Measure5.2 Trigonometric Functions: Unit Circle Approach5.3 Properties of the Trigonometric Functions5.4 Graphs of the Sine and Cosine Functions5.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions5.6 Phase Shift; Sinusoidal Curve Fitting Chapter Review Chapter Test Chapter Projects Cumulative Review 6. Analytic Trigonometry6.1 The Inverse Sine, Cosine, and Tangent Functions6.2 The Inverse Trigonometric Functions (Continued)6.3 Trigonometric Identities6.4 Sum and Difference Formulas6.5 Double-angle and Half-angle Formulas6.6 Product-to-Sum and Sum-to-Product Formulas6.7 Trigonometric Equations Chapter Review Chapter Test Chapter Projects Cumulative Review 7. Applications of Trigonometric Functions7.1 Applications Involving Right Triangles7.2 The Law of Sines7.3 The Law of Cosines7.4 Area of a Triangle7.5 Simple Harmonic Motion; Damped Motion; Combining Waves Chapter Review Chapter Test Chapter Projects Cumulative Review 8. Polar Coordinates; Vectors8.1 Polar Coordinates8.2 Polar Equations and Graphs8.3 The Complex Plane; DeMoivre's Theorem8.4 Vectors8.5 The Dot Product8.6 Vectors in Space8.7 The Cross Product Chapter Review Chapter Test Chapter Projects Cumulative Review 9. Analytic Geometry9.1 Conics9.2 The Parabola9.3 The Ellipse9.4 The Hyperbola9.5 Rotation of Axes; General Form of a Conic9.6 Polar Equations of Conics9.7 Plane Curves and Parametric Equations Chapter Review Chapter Test Chapter Projects Cumulative Review 10. Systems of Equations and Inequalities10.1 Systems of Linear Equations: Substitution and Elimination10.2 Systems of Linear Equations: Matrices10.3 Systems of Linear Equations: Determinants10.4 Matrix Algebra10.5 Partial Fraction Decomposition10.6 Systems of Nonlinear Equations10.7 Systems of Inequalities10.8 Linear Programming Chapter Review Chapter Test Chapter Projects Cumulative Review 11. Sequences; Induction; the Binomial Theorem11.1 Sequences11.2 Arithmetic Sequences11.3 Geometric Sequences; Geometric Series11.4 Mathematical Induction11.5 The Binomial Theorem Chapter Review Chapter Test Chapter Projects Cumulative Review 12. Counting and Probability12.1 Counting12.2 Permutations and Combinations12.3 Probability Chapter Review Chapter Test Chapter Projects Cumulative Review 13. A Preview of Calculus: The Limit; Derivative, and Integral of a Function13.1 Finding Limits Using Tables and Graphs13.2 Algebra Techniques for Finding Limits13.3 One-sided Limits; Continuous Functions13.4 The Tangent Problem; The Derivative13.5 The Area Problem; The Integral Chapter Review Chapter Test Chapter Projects Cumulative Review Appendix A. ReviewA.1 Algebra EssentialsA.2 Geometry EssentialsA.3 PolynomialsA.4 Factoring PolynomialsA.5 Synthetic DivisionA.6 Rational ExpressionsA.7 nth Roots; Rational ExponentsA.8 Solving EquationsA.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate JobsA.10 Interval Notation; Solving InequalitiesA.11 Complex Numbers Appendix B. Graphing UtilitiesB.1 The Viewing RectangleB.2 Using a Graphing Utility to Graph EquationsB.3 Using a Graphing Utility to Locate Intercepts and Check for SymmetryB.4 Using a Graphing Utility to Solve EquationsB.5 Square ScreensB.6 Using a Graphing Utility to Graph InequalitiesB.7 Using a Graphing Utility to Solve Systems of Linear EquationsB.8 Using a Graphing Utility to Graph a Polar EquationB.9 Using a Graphing Utility to Graph Parametric Equations AnswersIndex