| |

| |

Preface to the Instructor | |

| |

| |

List of Applications | |

| |

| |

Photo Credits | |

| |

| |

To the Student | |

| |

| |

| |

Graphs | |

| |

| |

| |

The Distance and Midpoint Formulas | |

| |

| |

| |

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

| |

| |

| |

Lines | |

| |

| |

| |

Circles | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Chapter Projects | |

| |

| |

| |

Functions and Their Graphs | |

| |

| |

| |

Functions | |

| |

| |

| |

The Graph of a Function | |

| |

| |

| |

Properties of Functions | |

| |

| |

| |

Library of Functions; Piecewise-defined Functions | |

| |

| |

| |

Graphing Techniques: Transformations | |

| |

| |

| |

Mathematical Models: Building Functions | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Linear and Quadratic Functions | |

| |

| |

| |

Linear Functions and Their Properties | |

| |

| |

| |

Building Linear Functions from Data | |

| |

| |

| |

Quadratic Functions and Their Properties | |

| |

| |

| |

Quadratic Models; Building Quadratic Functions from Data | |

| |

| |

| |

Inequalities Involving Quadratic Functions | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Polynomial and Rational Functions | |

| |

| |

| |

Polynomial Functions and Models | |

| |

| |

| |

Properties of Rational Functions | |

| |

| |

| |

The Graph of a Rational Function | |

| |

| |

| |

Polynomial and Rational Inequalities | |

| |

| |

| |

The Real Zeros of a Polynomial Function | |

| |

| |

| |

Complex Zeros; Fundamental Theorem of Algebra | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Exponential and Logarithmic Functions | |

| |

| |

| |

Composite Functions | |

| |

| |

| |

One-to-One Functions; Inverse Functions | |

| |

| |

| |

Exponential Functions | |

| |

| |

| |

Logarithmic Functions | |

| |

| |

| |

Properties of Logarithms | |

| |

| |

| |

Logarithmic and Exponential Equations | |

| |

| |

| |

Compound Interest | |

| |

| |

| |

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

| |

| |

| |

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

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Trigonometric Functions | |

| |

| |

| |

Angles and Their Measure | |

| |

| |

| |

Trigonometric Functions: Unit Circle Approach | |

| |

| |

| |

Properties of the Trigonometric Functions | |

| |

| |

| |

Graphs of the Sine and Cosine Functions | |

| |

| |

| |

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

| |

| |

| |

Phase Shift; Sinusoidal Curve Fitting | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Analytic Trigonometry | |

| |

| |

| |

The Inverse Sine, Cosine, and Tangent Functions | |

| |

| |

| |

The Inverse Trigonometric Functions (Continued) | |

| |

| |

| |

Trigonometric Identities | |

| |

| |

| |

Sum and Difference Formulas | |

| |

| |

| |

Double-angle and Half-angle Formulas | |

| |

| |

| |

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

| |

| |

| |

Trigonometric Equations (I) | |

| |

| |

| |

Trigonometric Equations (II) | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Applications of Trigonometric Functions | |

| |

| |

| |

Applications Involving Right Triangles | |

| |

| |

| |

The Law of Sines | |

| |

| |

| |

The Law of Cosines | |

| |

| |

| |

Area of a Triangle | |

| |

| |

| |

Simple Harmonic Motion; Damped Motion; Combining Waves | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Polar Coordinates; Vectors | |

| |

| |

| |

Polar Coordinates | |

| |

| |

| |

Polar Equations and Graphs | |

| |

| |

| |

The Complex Plane; DeMoivre's Theorem | |

| |

| |

| |

Vectors | |

| |

| |

| |

The Dot Product | |

| |

| |

| |

Vectors in Space | |

| |

| |

| |

The Cross Product | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Analytic Geometry | |

| |

| |

| |

Conics | |

| |

| |

| |

The Parabola | |

| |

| |

| |

The Ellipse | |

| |

| |

| |

The Hyperbola | |

| |

| |

| |

Rotation of Axes; General Form of a Conic | |

| |

| |

| |

Polar Equations of Conics | |

| |

| |

| |

Plane Curves and Parametric Equations | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Systems of Equations and Inequalities | |

| |

| |

| |

Systems of Linear Equations: Substitution and Elimination | |

| |

| |

| |

Systems of Linear Equations: Matrices | |

| |

| |

| |

Systems of Linear Equations: Determinants | |

| |

| |

| |

Matrix Algebra | |

| |

| |

| |

Partial Fraction Decomposition | |

| |

| |

| |

Systems of Nonlinear Equations | |

| |

| |

| |

Systems of Inequalities | |

| |

| |

| |

Linear Programming | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Sequences; Induction; the Binomial Theorem | |

| |

| |

| |

Sequences | |

| |

| |

| |

Arithmetic Sequences | |

| |

| |

| |

Geometric Sequences; Geometric Series | |

| |

| |

| |

Mathematical Induction | |

| |

| |

| |

The Binomial Theorem | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

Counting and Probability | |

| |

| |

| |

Counting | |

| |

| |

| |

Permutations and Combinations | |

| |

| |

| |

Probability | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Cumulative Review | |

| |

| |

Chapter Projects | |

| |

| |

| |

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

| |

| |

| |

Finding Limits Using Tables and Graphs | |

| |

| |

| |

Algebra Techniques for Finding Limits | |

| |

| |

| |

One-sided Limits; Continuous Functions | |

| |

| |

| |

The Tangent Problem; The Derivative | |

| |

| |

| |

The Area Problem; The Integral | |

| |

| |

Chapter Review | |

| |

| |

Chapter Test | |

| |

| |

Chapter Projects | |

| |

| |

| |

Review | |

| |

| |

| |

Algebra Essentials | |

| |

| |

| |

Geometry Essentials | |

| |

| |

| |

Polynomials | |

| |

| |

| |

Synthetic Division | |

| |

| |

| |

Rational Expressions | |

| |

| |

| |

Solving Equations | |

| |

| |

| |

Complex Numbers; Quadratic Equations in the Complex Number System | |

| |

| |

| |

Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications | |

| |

| |

| |

Interval Notation; Solving Inequalities | |

| |

| |

| |

nth Roots; Rational Exponents | |

| |

| |

| |

Graphing Utilities | |

| |

| |

| |

The Viewing Rectangle | |

| |

| |

| |

Using a Graphing Utility to Graph Equations | |

| |

| |

| |

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

| |

| |

| |

Using a Graphing Utility to Solve Equations | |

| |

| |

| |

Square Screens | |

| |

| |

| |

Using a Graphing Utility to Graph Inequalities | |

| |

| |

| |

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

| |

| |

| |

Using a Graphing Utility to Graph a Polar Equation | |

| |

| |

| |

Using a Graphing Utility to Graph Parametric Equations | |

| |

| |

Answers | |

| |

| |

Index | |