Precalculus

Mike Sullivan Professor of Mathematics at Chicago State University received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 35 years.  He has been writing textbooks in mathematics for over 30 years. Mike has authored or co-authored over ten books. He is a native of Chicago’s South Side and currently resides in Oaklawn. He has four children: Kathleen, who teaches college mathematics, Mike III, who co-authors many titles as well as teaches college mathematics, Dan, who is a Prentice Hall sales representative, and Colleen, who teaches middle-school mathematics. Nine grandchildren round out the family.   Why I Wrote This Book:   As a professor of mathematics at an urban public university for over 35 years, I understand the varied needs of precalculus students who range from having little mathematical background and a fear of mathematics courses to those who have had a strong mathematical education and are highly motivated.  For some of your students, this will be their last course in mathematics, while others may decide to further their mathematical education.  I have written this text for both groups.  As the author of precalculus, engineering calculus, finite math and business calculus texts, and, as a teacher, I understand what students must know if they are to be focused and successful in upper level mathematics courses.  However, as a father of four, I also understand the realities of college life.  I have taken great pains to insure that this text contains solid, student-friendly examples and problems, as well as a clear writing style.  I encourage you to share with me your experiences teaching from this text.   The eighth edition of this series builds upon a solid foundation by integrating new features and techniques that further enhance student interest and involvement.  The elements of the previous edition that have proved successful remain, while many changes, some obvious, others subtle, have been made.  A huge benefit of authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based.  Virtually every change to this edition is the result of thoughtful comments and suggestions made from colleagues and students who have used the previous edition.  I am sincerely grateful for this feedback and have tried to make changes that improve the flow and usability of this text.

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 Review

Chapter Test

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

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 Review

Chapter Test

Cumulative Review

Chapter Projects

 

Chapter 13  Counting and Probability

13.1 Sets and Counting

13.2 Permutations and Combinations

13.3 Probability

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

 

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

Chapter Review

Chapter Test

Chapter Projects

 

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