## Table of Contents

**R. Review**

R.1 Real Numbers

R.2 Algebra Essentials

R.3 Geometry Essentials

R.4 Polynomials

R.5 Factoring Polynomials

R.6 Synthetic Division

R.7 Rational Expressions

R.8 *n*th Roots; Rational Exponents

**1. Equations and Inequalities**1.1 Linear Equations

1.2 Quadratic Equations

1.3 Complex Numbers; Quadratic Equations in the Complex Number System

1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations

1.5 Solving Inequalities

1.6 Equations and Inequalities Involving Absolute Value

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

Chapter 1 Review, Test, and Projects

**2. Graphs**2.1 The Distance and Midpoint Formulas

2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

2.3 Lines

2.4 Circles

2.5 Variation

Chapter 2 Review, Test, and Projects

**3. Functions and Their Graphs**3.1 Functions

3.2 The Graph of a Function

3.3 Properties of Functions

3.4 Library of Functions; Piecewise-defined Functions

3.5 Graphing Techniques: Transformations

3.6 Mathematical Models: Building Functions

Chapter 3 Review, Test, and Projects

4. Linear and Quadratic Functions

4.1 Properties of Linear Functions and Linear Models

4.2 Building Linear Models from Data

4.3 Quadratic Functions and Their Properties

4.4 Build Quadratic Models from Verbal Descriptions and from Data

4.5 Inequalities Involving Quadratic Functions

Chapter 4 Review, Test, and Projects

**5. Polynomial and Rational Functions**5.1 Polynomial Functions

5.2 Graphing Polynomials Functions; Models

5.3 Properties of Rational Functions

5.4 The Graph of a Rational Function

5.5 Polynomial and Rational Inequalities

5.6 The Real Zeros of a Polynomial Function

Chapter 5 Review, Test, and Projects

**6. Exponential and Logarithmic Functions**6.1 Composite Functions

6.2 One-to-One Functions; Inverse Functions

6.3 Exponential Functions

6.4 Logarithmic Functions

6.5 Properties of Logarithms

6.6 Logarithmic and Exponential Equations

6.7 Financial Models

6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models

6.9 Building Exponential, Logarithmic, and Logistic Models from Data

Chapter 6 Review, Test, and Projects

**7. Analytic Geometry**7.1 Conics

7.2 The Parabola

7.3 The Ellipse

7.4 The Hyperbola

Chapter 7 Review, Test, and Projects

**8. Systems of Equations and Inequalities**8.1 Systems of Linear Equations: Substitution and Elimination

8.2 Systems of Linear Equations: Matrices

8.3 Systems of Linear Equations: Determinants

8.4 Matrix Algebra

8.5 Partial Fraction Decomposition

8.6 Systems of Nonlinear Equations

8.7 Systems of Inequalities

8.8 Linear Programming

Chapter 8 Review, Test, and Projects

**9. Sequences; Induction; the Binomial Theorem**9.1 Sequences

9.2 Arithmetic Sequences

9.3 Geometric Sequences; Geometric Series

9.4 Mathematical Induction

9.5 The Binomial Theorem

Chapter 9 Review, Test, and Projects

**10. Counting and Probability**10.1 Counting

10.2 Permutations and Combinations

10.3 Probability

Chapter 10 Review, Test, and Projects

**Appendix: Graphing Utilities**

A.1 The Viewing Rectangle

A.2 Using a Graphing Utility to Graph Equations

A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry

A.4 Using a Graphing Utility to Solve Equations

A.5 Square Screens

A.6 Using a Graphing Utility to Graph Inequalities

A.7 Using a Graphing Utility to Solve Systems of Linear Equations