## Table of Contents

**Foundations: A Prelude to Functions**

F.1 The Distance and Midpoint Formulas

F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

F.3 Lines

F.4 Circles

**1. Functions and Their Graphs**

1.1 Functions

1.2 The Graph of a Function

1.3 Properties of Functions

1.4 Library of Functions; Piecewise-defined Functions

1.5 Graphing Techniques: Transformations

1.6 Mathematical Models: Constructing Functions

1.7 Building Mathematical Models Using Variation

Chapter Review

Chapter Test

Chapter Projects

**2. Linear and Quadratic Functions**

2.1 Properties of Linear Functions and Linear Models

2.2 Building Linear Models from Data

2.3 Quadratic Functions and Their Zeros

2.4 Properties of Quadratic Functions

2.5 Inequalities Involving Quadratic Functions

2.6 Building Quadratic Models from Verbal Descriptions and from Data

2.7 Complex Zeros of a Quadratic Function

2.8 Equations and Inequalities Involving the Absolute Value Function

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**3. Polynomial and Rational Functions**

3.1 Polynomial Functions and Models

3.2 Properties of Rational Functions

3.3 The Graph of a Rational Function

3.4 Polynomial and Rational Inequalities

3.5 The Real Zeros of a Polynomial Function

3.6 Complex Zeros; Fundamental Theorem of Algebra

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**4. Exponential and Logarithmic Functions**

4.1 Composite Functions

4.2 One-to-One Functions; Inverse Functions

4.3 Exponential Functions

4.4 Logarithmic Functions

4.5 Properties of Logarithms

4.6 Logarithmic and Exponential Equations

4.7 Compound Interest

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

4.9 Building Exponential, Logarithmic, and Logistic Functions from Data

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**5. Trigonometric Functions**

5.1 Angles and Their Measure

5.2 Trigonometric Functions: Unit Circle Approach

5.3 Properties of the Trigonometric Functions

5.4 Graphs of the Sine and Cosine Functions

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

5.6 Phase Shift; Sinusoidal Curve Fitting

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**6. Analytic Trigonometry**

6.1 The Inverse Sine, Cosine, and Tangent Functions

6.2 The Inverse Trigonometric Functions (Continued)

6.3 Trigonometric Equations

6.4 Trigonometric Identities

6.5 Sum and Difference Formulas

6.6 Double-angle and Half-angle Formulas

6.7 Product-to-Sum and Sum-to-Product Formulas

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**7. Applications of Trigonometric Functions**

7.1 Right Triangle Trigonometry; Applications Involving Right Triangles

7.2 The Law of Sines

7.3 The Law of Cosines

7.4 Area of a Triangle

7.5 Simple Harmonic Motion; Damped Motion; Combining Waves

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**8. Polar Coordinates; Vectors**

8.1 Polar Coordinates

8.2 Polar Equations and Graphs

8.3 The Complex Plane; DeMoivre's Theorem

8.4 Vectors

8.5 The Dot Product

8.6 Vectors in Space

8.7 The Cross Product

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**9. Analytic Geometry**

9.1 Conics

9.2 The Parabola

9.3 The Ellipse

9.4 The Hyperbola

9.5 Rotation of Axes; General Form of a Conic

9.6 Polar Equations of Conics

9.7 Plane Curves and Parametric Equations

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**10. Systems of Equations and Inequalities**

10.1 Systems of Linear Equations: Substitution and Elimination

10.2 Systems of Linear Equations: Matrices

10.3 Systems of Linear Equations: Determinants

10.4 Matrix Algebra

10.5 Partial Fraction Decomposition

10.6 Systems of Nonlinear Equations

10.7 Systems of Inequalities

10.8 Linear Programming

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**11. Sequences; Induction; the Binomial Theorem**

11.1 Sequences

11.2 Arithmetic Sequences

11.3 Geometric Sequences; Geometric Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**12. Counting and Probability**

12.1 Counting

12.2 Permutations and Combinations

12.3 Probability

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**13. A Preview of Calculus: The Limit; Derivative, and Integral of a Function**

13.1 Finding Limits Using Tables and Graphs

13.2 Algebra Techniques for Finding Limits

13.3 One-sided Limits; Continuous Functions

13.4 The Tangent Problem; The Derivative

13.5 The Area Problem; The Integral

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

**Appendix A. Review**

A.1 Algebra Essentials

A.2 Geometry Essentials

A.3 Polynomials

A.4 Factoring Polynomials

A.5 Synthetic Division

A.6 Rational Expressions

A.7 *n*th Roots; Rational Exponents

A.8 Solving Equations

A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs

A.10 Interval Notation; Solving Inequalities

A.11 Complex Numbers

**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

Answers

Index