## Table of Contents

**Chapter 1 Graphs**

1.1 Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations

1.2 Intercepts; Symmetry; Graphing Key Equations

1.3 Solving Equations Using a Graphing Utility

1.4 Lines

1.5 Circles

**Chapter 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

**Chapter 3 Linear and Quadratic Functions**

3.1 Linear Functions, Their Properties, and Linear Models

3.2 Building Linear Models from Data; Direct Variation

3.3 Quadratic Functions and Their Properties

3.4 Building Quadratic Models from Verbal Descriptions and Data

3.5 Inequalities Involving Quadratic Functions

**Chapter 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

**Chapter 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

**Chapter 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; Building Sinusoidal Models

**Chapter 7 Analytic Trigonometry**

7.1 The Inverse Sine, Cosine, and Tangent Functions

7.2 The Inverse Trigonometric Functions (Continued)

7.3 Trigonometric Identities

7.4 Sum and Difference Formulas

7.5 Double-angle and Half-angle Formulas

7.6 Product-to-Sum and Sum-to-Product Formulas

7.7 Trigonometric Equations (I)

7.8 Trigonometric Equations (II)

**Chapter 8 Applications of Trigonometric Functions**

8.1 Applications Involving Right Triangles

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

**Chapter 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

**Chapter 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

** **

**Chapter 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

**Chapter 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

**Chapter 13 Counting and Probability**

13.1 Counting

13.2 Permutations and Combinations

13.3 Probability

**Chapter 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-side 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 *n*th Roots; Rational Exponents

**Appendix B The Limit of a Sequence; Infinite Series**