## 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 nth 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, and Constant Rate Job Applications

**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

**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

**4. Linear and Quadratic Functions**

4.1 Linear Functions and Their Properties

4.2 Building Linear Functions from Data

4.3 Quadratic Functions and Their Properties

4.4 Quadratic Models; Building Quadratic Functions from Data

4.5 Inequalities Involving Quadratic Functions

**5. Polynomial and Rational Functions**

5.1 Polynomial Functions and Models

5.2 Properties of Rational Functions

5.3 The Graph of a Rational Function

5.4 Polynomial and Rational Inequalities

5.5 The Real Zeros of a Polynomial Function

5.6 Complex Zeros: Fundamental Theorem of Algebra

**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 Compound Interest

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

6.9 Building Exponential, Logarithmic, and Logistic Functions from Data

**7. Analytic Geometry**

7.1 Conics

7.2 The Parabola

7.3 The Ellipse

7.4 The Hyperbola

**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

**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

**10. Counting and Probability**

10.1 Sets and Counting

10.2 Permutations and Combinations

10.3 Probability

**Appendix: Graphing Utilities**

1 The Viewing Rectangle

2 Using a Graphing Utility to Graph Equations

3 Using a Graphing Utility to Graph Equations Locating Intercepts and Checking for Symmetry

4 Using a Graphing Utility to Solve Equations

5 Square Screens

6 Using a Graphing Utility to Graph Inequalities

7 Using a Graphing Utility to Solve Systems of Linear Equations