## Table of Contents

**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 (Sections 1.1–1.2)

1.3 Linear Functions

1.4 Equations of Lines and Linear Models

Reviewing Basic Concepts (Sections 1.3–1.4)

1.5 Linear Equations and Inequalities

Unifying Linear Functions

1.6 Applications of Linear Functions

Reviewing Basic Concepts (Sections 1.5–1.6)

Summary

Review Exercises

Test

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 (Sections 2.1–2.3)

2.4 Absolute Value Functions

Unifying Absolute Value Functions

2.5 Piecewise-Defined Functions

2.6 Operations and Composition

Reviewing Basic Concepts (Sections 2.4–2.6)

Summary

Review Exercises

Test

3. Quadratic Functions

3.1 Complex Numbers

3.2 Quadratic Functions and Graphs

Reviewing Basic Concepts (Sections 3.1–3.2)

3.3 Quadratic Equations and Inequalities

Unifying Quadratic Functions

3.4 Applications of Quadratic Functions and Models

Reviewing Basic Concepts (Sections 3.3–3.4)

Summary

Review Exercises

Test

4. Polynomial Functions of Higher Degree

4.1 Graphs of Polynomial Functions

4.2 Topics in the Theory of Polynomial Functions (I)

Reviewing Basic Concepts (Sections 4.1–4.2)

4.3 Topics in the Theory of Polynomial Functions (II)

4.4 Polynomial Equations, Inequalities, Applications, and Models

Reviewing Basic Concepts (Sections 4.3–4.4)

Unifying Polynomial Functions

Summary

Review Exercises

Test

**5. Rational, Power, and Root Functions**

5.1 Rational Functions and Graphs (I)

5.2 Rational Functions and Graphs (II)

5.3 Rational Equations, Inequalities, Models, and Applications

5.4 Functions Defined by Powers and Roots

5.5 Equations, Inequalities, and Applications Involving Root Functions

Reviewing Basic Concepts (Sections 5.4–5.5)

Unifying Root Functions

Summary

Review Exercises

Test

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

6.1 Inverse Functions

6.2 Exponential Functions

6.3 Logarithms and Their Properties

6.4 Logarithmic Functions

6.5 Exponential and Logarithmic Equations and Inequalities

6.6 Further Applications and Modeling with Exponential and Logarithmic Functions

Reviewing Basic Concepts (Sections 6.4–6.6)

Summary

Review Exercises

Test

**7. Systems and 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 (Sections 7.1–7.3)

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 (Sections 7.4–7.6)

7.7 Systems of Inequalities and Linear Programming

7.8 Partial Fractions

Reviewing Basic Concepts (Sections 7.7–7.8)

Summary

Review Exercises

Test

**8. Conic Sections, Nonlinear Systems, and Parametric Equations**

8.1 Circles Revisited and Parabolas

8.2 Ellipses and Hyperbolas

Reviewing Basic Concepts (Sections 8.1–8.2)

8.3 The Conic Sections and Nonlinear Systems

8.4 Introduction to Parametric Equations

Reviewing Basic Concepts (Sections 8.3–8.4)

Summary

Review Exercises

Test

**9. Further Topics in Algebra**

9.1 Sequences and Series

9.2 Arithmetic Sequences and Series

9.3 Geometric Sequences and Series

Reviewing Basic Concepts (Sections 9.1–9.3)

9.4 Counting Theory

9.5 The Binomial Theorem

Reviewing Basic Concepts (Sections 9.4–9.5)

9.6 Mathematical Induction

9.7 Probability

Reviewing Basic Concepts (Sections 9.6–9.7)

Summary

Review Exercises

Test

**R. Review: Basic Algebraic Concepts**

R.2 Review of Exponents and Polynomials

R.3 Review of Factoring

R.4 Review of Rational Expressions

R.5 Review of Negative and Rational Exponents

R.6 Review of Radicals

*Test*

Appendix: Formulas from Geometry

Instructor’s Answers

Answers to Selected Exercises*

Index

*In the AIE, Instructor’s Answers replaces Answers to Selected Exercises.