## Table of Contents

**R. Review of Basic Concepts.**

Sets.

Real Numbers and Their Properties.

Polynomials.

Factoring Polynomials.

Rational Expressions.

Rational Exponents.

Radical Expressions.

**1. Equations and Inequalities.**

Linear Equations.

Applications and Modeling with Linear Equations.

Complex Numbers.

Quadratic Equations.

Applications and Modeling with Quadratic Equations.

Other Types of Equations and Applications.

Inequalities.

Absolute Value Equations and Inequalities.

**2. Graphs and Functions.**

Rectangular Coordinates and Graphs.

Circles.

Functions.

Linear Functions.

Equations of Lines; Curve Fitting.

Graphs of Basic Functions.

Graphing Techniques.

Function Operations and Composition.

**3. Polynomial and Rational Functions.**

Quadratic Functions and Models.

Synthetic Division.

Zeros of Polynomial Functions.

Polynomial Functions: Graphs, Applications, and Models.

Rational Functions: Graphs, Applications, and Models.

Variation.

**4. Inverse, Exponential, and Logarithmic Functions.**

Inverse Functions.

Exponential Functions.

Logarithmic Functions.

Evaluating Logarithms and the Change-of-Base Theorem.

Exponential and Logarithmic Equations.

Applications and Models of Exponential Growth and Decay.

**5. Systems and Matrices.**

Systems of Linear Equations.

Matrix Solution of Linear Systems.

Determinant Solution of Linear Systems.

Partial Fractions.

Nonlinear Systems of Equations.

Systems of Inequalities and Linear Programming.

Properties of Matrices.

Matrix Inverses.

**6. Analytic Geometry.**

Parabolas.

Ellipses.

Hyperbolas.

Summary of the Conic Sections.

**7. Further Topics in Algebra.**

Sequences and Series.

Arithmetic Sequences and Series.

Geometric Sequences and Series.

The Binomial Theorem.

Mathematical Induction.

Counting Theory.

Basics of Probability.

Glossary.

Solutions to Selected Exercises.

Answers to Selected Exercises.

Index of Applications.

Index.