## 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

Reviewing Basic Concepts (Sections 5.1–5.3)

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

Unifying Exponential Functions

6.3 Logarithms and Their Properties

Reviewing Basic Concepts (Sections 6.1ndash;6.3)

6.4 Logarithmic Functions

6.5 Exponential and Logarithmic Equations and Inequalities

Unifying Logarithmic Functions

6.6 Further Applications and Modeling with Exponential and Logarithmic Functions

Reviewing Basic Concepts (Sections 6.4–6.6)

Summary Exercises on Functions: Domains, Defining Equations, and Composition

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. The Unit Circle and the Functions of Trigonometry**

9.1 Angles, Arcs, and Their Measures

9.2 The Unit Circle and Its Functions

9.3 Graphs of the Sine and Cosine Functions

9.4 Graphs of the Other Circular Functions

9.5 Functions of Angles and Fundamental Angles

9.6 Evaluating Trigonometric Functions

9.7 Applications of Right Triangles

9.8 Harmonic Motion

Summary

Review Exercises

Test

**10. Trigonometric Identities and Equations**

10.1 Trigonometric Identities

10.2 Sum and Difference Identities

10.3 Further Identities

10.4 The Inverse Circular Functions

10.5 Trigonometric Equations and Inequalities (I)

10.6 Trigonometric Equations and Inequalities (II)

Unifying Trigonometric Functions

Summary

Review Exercises

Test

**11. Applications of Trigonometry and Vectors**

11.1 The Law of Sines

11.2 The Law of Cosines and Area Formulas

11.3 Vectors and Their Applications

11.4 Trigonometric (Polar) Form of Complex Numbers

11.5 Powers and Roots of Complex Numbers

11.6 Polar Equations and Graphs

11.7 More Parametric Equations

Summary

Review Exercises

Test

**12. Further Topics in Algebra**

12.1 Sequences and Series

12.2 Arithmetic Sequences and Series

12.3 Geometric Sequences and Series

Reviewing Basic Concepts (Sections 9.1–9.3)

12.4 Counting Theory

12.5 The Binomial Theorem

Reviewing Basic Concepts (Sections 9.4–9.5)

12.6 Mathematical Induction

12.7 Probability

Reviewing Basic Concepts (Sections 9.6–9.7)

Summary

Review Exercises

Test

**13. Limits, Derivatives, and Definite Integrals**

13.1 An Introduction to Limits

13.2 Techniques for Calculating Limits

13.3 One-Sided Limits and Limits Involving Infinity

13.4 Tangent Lines and Derivatives

13.5 Area and the Definite Integral

**R. Review: Basic Algebraic Concepts**

R.1 Review of Sets

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 A: Geometry Formulas

Appendix B: Vectors in Space

Appendix C: Polar Form of Conic Sections

Appendix D: Rotation of Axes

Instructor’s Answers

Answers to Selected Exercises*

Index

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