Precalculus, The MyLab Math Edition

TABLE OF CONTENTS

 

Chapter 1 Graphs

1.1 The Distance and Midpoint Formulas

1.2 Graphs of Equations; Intercepts; Symmetry

1.3 Lines

1.4 Circles

 

Chapter 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

 

Chapter 3 Linear and Quadratic Functions

3.1 Linear Functions and Their Properties

3.2 Building Linear Functions from Data

3.3 Quadratic Functions and Their Properties

3.4 Quadratic Models; Building Quadratic Functions From Data

3.5 Inequalities Involving Quadratic Functions

 

Chapter 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

 

Chapter 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 Compound Interest

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

5 .9 Building Exponential, Logarithmic, and Logistic Functions from Data

 

Chapter 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; Building Sinusoidal Functions from Data

 

Chapter 7   Analytic Trigonometry

7.1 The Inverse Sine, Cosine, and Tangent Functions

7.2 The Inverse Trigonometric Functions (continued)

7.3 Trigonometric Identities

7.4 Sum and Difference Formulas

7.5 Double-Angle and Half-Angle Formulas

7.6 Product-to-Sum and Sum-to-Product Formulas

7.7 Trigonometric Equations (I)

7.8 Trigonometric Equations (II)

 

Chapter 8   Applications of Trigonometric Functions

8.1 Right Triangle Trigonometry; Applications

8.2 Law of Sines

8.3 Law of Cosines

8.4 Area of a Triangle

8.5 Simple Harmonic Motion; Damped Motion; Combining Waves

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 13  Counting and Probability

13.1 Sets and Counting

13.2 Permutations and Combinations

13.3 Probability

 

Chapter 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



 

Appendix A Review  

A1 Algebra Essentials

A.2 Geometry Essentials

A.3 Polynomials and Rational Expressions

A.4 Polynomial Division; Synthetic Division

A.5 Solving Equations

A.6 Complex Numbers; Quadratic Equations in the Complex Number System

A.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Jobs Applications

A.8 Interval Notation; Solving Inequalities

A.9 nth Roots; Rational Exponents; Radical Equations

 

 

Appendix B Graphing Utilities

 

B.1 The Viewing Rectangle

B.2 Graphing Equations in Two Variables

B.3 Locating Intercepts and Checking for Symmetry

B.4 Solving Equations Using a Graphing Utility

B.5 Square Screens

B.6 Graphing Inequalities in Two Variables

B.7 Solving Systems of Linear Equations

B.8 Graphing a Polar Equation

B.9 Graphing Parametric Equations