## Table of Contents

**1. Graphs**

1.1 The Distance and Midpoint Formulas

1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

1.3 Lines

1.4 Circles

**2. Functions and Their Graphs**

2.1 Functions

2.2 The Graph of a Function

2.3 Properties of Functions

2.4 Library of Functions; Piecewise-defined Functions

2.5 Graphing Techniques: Transformations

2.6 Mathematical Models: Building Functions

**3. Linear and Quadratic Functions**

3.1 Properties of Linear Functions and Linear Models

3.2 Building Linear Models from Data

3.3 Quadratic Functions and Their Properties

3.4 Build Quadratic Models from Verbal Descriptions and from Data

3.5 Inequalities Involving Quadratic Functions

**4. Polynomial and Rational Functions**

4.1 Polynomial Functions and Models

4.2 Properties of Rational Functions

4.3 The Graph of a Rational Function

4.4 Polynomial and Rational Inequalities

4.5 The Real Zeros of a Polynomial Function

4.6 Complex Zeros; Fundamental Theorem of Algebra

**5. Exponential and Logarithmic Functions**

5.1 Composite Functions

5.2 One-to-One Functions; Inverse Functions

5.3 Exponential Functions

5.4 Logarithmic Functions

5.5 Properties of Logarithms

5.6 Logarithmic and Exponential Equations

5.7 Financial Models

5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models

5.9 Building Exponential, Logarithmic, and Logistic Models from Data

**6. Trigonometric Functions**

6.1 Angles and Their Measure

6.2 Trigonometric Functions: Unit Circle Approach

6.3 Properties of the Trigonometric Functions

6.4 Graphs of the Sine and Cosine Functions

6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

6.6 Phase Shift; Sinusoidal Curve Fitting

**7. Analytic Trigonometry**

7.1 The Inverse Sine, Cosine, and Tangent Functions

7.2 The Inverse Trigonometric Functions (Continued)

7.3 Trigonometric Equations

7.4 Trigonometric Identities

7.5 Sum and Difference Formulas

7.6 Double-angle and Half-angle Formulas

7.7 Product-to-Sum and Sum-to-Product Formulas

**8. Applications of Trigonometric Functions**

8.1 Right Triangle Trigonometry; Applications

8.2 The Law of Sines

8.3 The Law of Cosines

8.4 Area of a Triangle

8.5 Simple Harmonic Motion; Damped Motion; Combining Waves

**9. Polar Coordinates; Vectors**

9.1 Polar Coordinates

9.2 Polar Equations and Graphs

9.3 The Complex Plane; DeMoivre’s Theorem

9.4 Vectors

9.5 The Dot Product

9.6 Vectors in Space

9.7 The Cross Product

**10. Analytic Geometry**

10.1 Conics

10.2 The Parabola

10.3 The Ellipse

10.4 The Hyperbola

10.5 Rotation of Axes; General Form of a Conic

10.6 Polar Equations of Conics

10.7 Plane Curves and Parametric Equations

**11. Systems of Equations and Inequalities**

11.1 Systems of Linear Equations: Substitution and Elimination

11.2 Systems of Linear Equations: Matrices

11.3 Systems of Linear Equations: Determinants

11.4 Matrix Algebra

11.5 Partial Fraction Decomposition

11.6 Systems of Nonlinear Equations

11.7 Systems of Inequalities

11.8 Linear Programming

**12. Sequences; Induction; the Binomial Theorem**

12.1 Sequences

12.2 Arithmetic Sequences

12.3 Geometric Sequences; Geometric Series

12.4 Mathematical Induction

12.5 The Binomial Theorem

**13. Counting and Probability**

13.1 Counting

13.2 Permutations and Combinations

13.3 Probability

**14. A Preview of Calculus: The Limit, Derivative, and Integral of a Function**

14.1 Finding Limits Using Tables and Graphs

14.2 Algebra Techniques for Finding Limits

14.3 One-sided Limits; Continuous Functions

14.4 The Tangent Problem; The Derivative

14.5 The Area Problem; The Integral

**Appendix A: Review**

A.1 Algebra Essentials

A.2 Geometry Essentials

A.3 Polynomials

A.4 Synthetic Division

A.5 Rational Expressions

A.6 Solving Equations

A.7 Complex Numbers; Quadratic Equations in the Complex Number System

A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications

A.9 Interval Notation; Solving Inequalities

A.10 nth Roots; Rational Exponents

**Appendix B: Graphing Utilities**

B.1 The Viewing Rectangle

B.2 Using a Graphing Utility to Graph Equations

B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry

B.4 Using a Graphing Utility to Solve Equations

B.5 Square Screens

B.6 Using a Graphing Utility to Graph Inequalities

B.7 Using a Graphing Utility to Solve Systems of Linear Equations

B.8 Using a Graphing Utility to Graph a Polar Equation

B.9 Using a Graphing Utility to Graph Parametric Equations