# Precalculus

## Table of Contents

Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, Proofs in Mathematics, and P.S. Problem Solving.

**1. Functions and Their Graphs **

1.1 Graphs of Equations

1.2 Linear Equations in Two Variables

1.3 Functions

1.4 Analyzing Graphs of Functions

1.5 A Library of Functions

1.6 Shifting, Reflecting, and Stretching Graphs

1.7 Combinations of Functions

1.8 Inverse Functions

1.9 Mathematical Modeling

**2. Polynomial and Rational Functions **

2.1 Quadratic Functions

2.2 Polynomial Functions of Higher Degree

2.3 Polynomial and Synthetic Division

2.4 Complex Numbers

2.5 Zeros of Polynomial Functions

2.6 Rational Functions

2.7 Partial Fractions

**3. Exponential and Logarithmic Functions **

3.1 Exponential Functions and Their Graphs

3.2 Logarithmic Functions and Their Graphs

3.3 Properties of Logarithms

3.4 Exponential and Logarithmic Equations

3.5 Exponential and Logarithmic Models

**4. Trigonometry **

4.1 Radian and Degree Measure

4.2 Trigonometric Functions: The Unit Circle

4.3 Right Triangle Trigonometry

4.4 Trigonometric Functions of Any Angle

4.5 Graphs of Sine and Cosine Functions

4.6 Graphs of Other Trigonometric Functions

4.7 Inverse Trigonometric Functions

4.8 Applications and Models

**5. Analytic Trigonometry **

5.1 Using Fundamental Identities

5.2 Verifying Trigonometric Identities

5.3 Solving Trigonometric Equations

5.4 Sum and Difference Formulas

5.5 Multiple-Angle and Product-to-Sum Formulas

**6. Additional Topics in Trigonometry **

6.1 Law of Sines

6.2 Law of Cosines

6.3 Vectors in the Plane

6.4 Vectors and Dot Products

6.5 Trigonometric Form of a Complex Number

**7. Systems of Equations and Inequalities **

7.1 Solving Systems of Equations

7.2 Two-Variable Linear Systems

7.3 Multivariable Linear Systems

7.4 Systems of Inequalities

7.5 Linear Programming

**8. Matrices and Determinants **

8.1 Matrices and Systems of Equations

8.2 Operations with Matrices

8.3 The Inverse of a Square Matrix

8.4 The Determinant of a Square Matrix

8.5 Applications of Matrices and Determinants

**9. Sequences, Series, and Probability **

9.1 Sequences and Series

9.2 Arithmetic Sequences and Partial Sums

9.3 Geometric Sequences and Series

9.4 Mathematical Induction

9.5 The Binomial Theorem

9.6 Counting Principles

9.7 Probability

**10. Topics in Analytic Geometry **

10.1 Lines

10.2 Introduction to Conics: Parabolas

10.3 Ellipses

10.4 Hyperbolas

10.5 Rotation of Conics

10.6 Parametric Equations

10.7 Polar Coordinates

10.8 Graphs of Polar Equations

10.9 Polar Equations of Conics

**Appendix A Review of Fundamental Concepts of Algebra **

A.1 Real Numbers and Their Properties

A.2 Exponents and Radicals

A.3 Polynomials and Factoring

A.4 Rational Expressions

A.5 Solving Equations

A.6 Solving Inequalities

A.7 Errors and the Algebra of Calculus

A.8 Graphical Representation of Data

**Answers to Odd-Numbered Exercises and Tests **

**Index of Applications**