## Table of Contents

**Chapter 1 Linear Functions, Equations, and Inequalities**

1.1 Real Numbers and the Rectangular Coordinate System

1.2 Introduction to Relations and Functions

Reviewing Basic Concepts

1.3 Linear Functions

1.4 Equations of Lines and Linear Models

Reviewing Basic Concepts

1.5 Linear Equations and Inequalities

1.6 Applications of Linear Functions

Reviewing Basic Concepts

Summary

Review Exercises

Test

**Chapter 2 Analysis of Graphs of Functions**

2.1 Graphs of Basic Functions and Relations; Symmetry

2.2 Vertical and Horizontal Shifts of Graphs

2.3 Stretching, Shrinking, and Reflecting Graphs

Reviewing Basic Concepts

2.4 Absolute Value Functions

2.5 Piecewise-Defined Functions

2.6 Operations and Composition

Reviewing Basic Concepts

Summary

Review Exercises

Test

**Chapter 3 Polynomial Functions**

3.1 Complex Numbers

3.2 Quadratic Functions and Graphs

3.3 Quadratic Equations and Inequalities

Reviewing Basic Concepts

3.4 Further Applications of Quadratic Functions and Models

3.5 Higher-Degree Polynomial Functions and Graphs

Reviewing Basic Concepts

3.6 Topics in the Theory of Polynomial Functions (I)

3.7 Topics in the Theory of Polynomial Functions (II)

3.8 Polynomial Equations and Inequalities; Further Applications and Models

Reviewing Basic Concepts

Summary

Review Exercises

Test

**Chapter 4 Rational, Power, and Root Functions**

4.1 Rational Functions and Graphs

4.2 More on Rational Functions and Graphs

4.3 Rational Equations, Inequalities, Models, and Applications

Reviewing Basic Concepts

4.4 Functions Defined by Powers and Roots

4.5 Equations, Inequalities, and Applications Involving Root Functions

Reviewing Basic Concepts

Summary

Review Exercises

Test

**Chapter 5 Inverse, Exponential, and Logarithmic Functions**

5.1 Inverse Functions

5.2 Exponential Functions

5.3 Logarithms and Their Properties

Reviewing Basic Concepts

5.4 Logarithmic Functions

5.5 Exponential and Logarithmic Equations and Inequalities

Reviewing Basic Concepts

5.6 Further Applications and Modeling with Exponential and Logarithmic Functions

Summary

Review Exercises

Test

**Chapter 6 Analytic Geometry**

6.1 Circles and Parabolas

6.2 Ellipses and Hyperbolas

Reviewing Basic Concepts

6.3 Summary of Conic Sections

6.4 Parametric Equations

Reviewing Basic Concepts

Summary

Review Exercises

Test

**Chapter 7 Systems of Equations and Inequalities; Matrices**

7.1 Systems of Equations

7.2 Solution of Linear Systems in Three Variables

7.3 Solution of Linear Systems by Row Transformations

Reviewing Basic Concepts

7.4 Matrix Properties and Operations

7.5 Determinants and Cramer’s Rule

7.6 Solution of Linear Systems by Matrix Inverses

Reviewing Basic Concepts

7.7 Systems of Inequalities and Linear Programming

7.8 Partial Fractions

Reviewing Basic Concepts

Summary

Review Exercises

Test

**Chapter 8 The Unit Circle and the Functions of Trigonometry**

8.1 Angles, Arcs, and Their Measures

8.2 The Unit Circle and Its Functions

Reviewing Basic Concepts

8.3 Graphs of the Sine and Cosine Functions

Periodic Functions

8.4 Graphs of the Other Circular Functions

8.5 Functions of Angles and Fundamental Identities

8.6 Evaluating Trigonometric Functions

Definitions of the Trigonometric Functions

8.7 Applications of Right Triangles

8.8 Harmonic Motion

Reviewing Basic Concepts

Summary

Review Exercises

Test

**Chapter 9 Trigonometric Identities and Equations **

9.1 Trigonometric Identities

9.2 Sum and Difference Identities

Reviewing Basic Concepts

9.3 Further Identities

9.4 The Inverse Circular Functions

Reviewing Basic Concepts

9.5 Trigonometric Equations and Inequalities (I)

9.6 Trigonometric Equations and Inequalities (II)

Summary

Review Exercises

Test

**Chapter 10 Applications of Trigonometry and Vectors**

10.1 The Law of Sines

10.2 The Law of Cosines and Area Formulas

10.3 Vectors and Their Applications

Reviewing Basic Concepts

10.4 Trigonometric (Polar) Form of Complex Numbers

10.5 Powers and Roots of Complex Numbers

Reviewing Basic Concepts

10.6 Polar Equations and Graphs

10.7 More Parametric Equations

Reviewing Basic Concepts

Summary

Review Exercises

Test

**Chapter 11 ****Further Topics in Algebra**

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

11.5 Mathematical Induction

11.6 Counting Theory

11.7 Probability

** **

**Chapter 12 Limits, Derivatives, and Definite Integrals**

12.1 An Introduction to Limits

12.2 Techniques for Calculating Limits

12.3 One-Sided Limits; Limits Involving Infinity

12.4 Tangent Lines and Derivatives

12.5 Area and the Definite Integral

** **

**Chapter R Reference: Basic Algebraic Concepts**

R.1 Review of Exponents and Polynomials

R.2 Review of Factoring

R.3 Review of Rational Expressions

R.4 Review of Negative and Rational Exponents

R.5 Review of Radicals

Chapter R Test

**Appendix Geometry Formulas**

**Answers to Selected Exercises**

**Index**