## 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 Jobs 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 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 Description and 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 Financial Models

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 Hyberbola

**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 Counting

10.2 Permutations and Combinations

10.3 Probability

**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