Algebra and Trigonometry Enhanced with Graphing Utilities

Prepare, Practice, Review

The Sullivan’s time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. The Enhanced with Graphing Utilities Series has evolved to meet today’s course needs by integrating the usage of graphing calculators, active-learning, and technology in new ways to help students be successful in their course, as well as in their future endeavors.

In the Seventh Edition, there are several new features that appear in both the text and MyMathLab. Retain Your Knowledge problems offer the type of “final exam material” that students can use to maintain their skills throughout each chapter.

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Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Mike taught at Chicago State for 35 years before recently retiring. He is a native of Chicago’s South Side and divides his time between Oak Lawn, Illinois, and Naples, Florida.

Mike is a member of the American Mathematical Society and the Mathematical Association of America. He is a past president of the Text and Academic Authors Association and is currently Treasurer of its Foundation. He is a member of the TAA Council of Fellows, and was awarded the TAA Mike Keedy award in 1997 and the Lifetime Achievement Award in 2007. In addition, he represents TAA on the Authors Coalition of America.

Mike has been writing textbooks for more than 35 years and currently has 15 books in print, 12 with Pearson Education. When not writing, he enjoys tennis, golf, gardening, and travel.

Mike has four children: Kathleen teaches college mathematics; Michael III teaches college mathematics and is his co-author on two precalculus series; Dan works in publishing; and Colleen teaches middle school and secondary school mathematics. Twelve grandchildren round out the family.

Mike Sullivan III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer, who tries to spend as much of his limited free time as possible on the golf course.

R. Review

R-1 Real Numbers

R-2 Algebra Essentials

R-3 Geometry Essentials

R-4 Polynomials

R-5 Factoring Polynomials

R-6 Synthetic Division

R-7 Rational Expressions

R-8 nth Roots; Rational Exponents

1. Graphs, Equations, and Inequalities

1-1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations

1-2 Solving Equations Using a Graphing Utility; Learning and Rational Equations

1-3 Quadratic Equation

1-4 Complex Numbers; Quadratic Equations in the Complex Number System

1-5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations

1-6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs

1-7 Solving Inequalities

Chapter Review

Chapter Test

Chapter Projects

2. Graphs

2-1 Intercepts: Syemmetry; Graphing Key Equations

2-2 Lines

2-3 Circles

2-4 Variation

Chapter Review

Chapter Test

Cumulative Review

Chapter Project

3. Functions and Their Graphs

3-1 Functions

3-2 The Graph of a Function

3-3 Properties of Functions

3-4 Library of Functions; Piecewise-defined Functions

3-5 Graphing Techniques: Transformations

3-6 Mathematical Models: Building Functions

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

4. Linear and Quadratic Functions

4-1 Properties of Linear Functions and Linear Models

4-2 Building Linear Models from Data

4-3 Quadratic Functions and Their Properties

4-4 Build Quadratic Models from Verbal Descriptions and from Data

4-5 Inequalities Involving Quadratic Functions

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

5. Polynomial and Rational Functions

5-1 Polynomial Functions and Models

5-2 The Real Zeros of a Polynomial Function

5-3 Complex Zeros; Fundamental Theorem of Algebra

5-4 Properties of Rational Functions

5-5 The Graph of a Rational Function

5-6 Polynomial and Rational Inequalities

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

6. Exponential and Logarithmic Functions

6-1 Composite Functions

6-2 One-to-One Functions; Inverse Functions

6-3 Exponential Functions

6-4 Logarithmic Functions

6-5 Properties of Logarithms

6-6 Logarithmic and Exponential Equations

6-7 Financial Models

6-8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models

6-9 Building Exponential, Logarithmic, and Logistic Models from Data

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

7. Trigonometric Functions

7-1 Angles and Their Measure

7-2 Right Triangle Trigonometry

7-3 Computing the Values of Trigonometric Functions of Acute Angles

7-4 Trigonometric Functions of Any Angle

7-5 Unit Circle Approach; Properties of the Trigonometric Functions

7-6 Graphs of the Sine and Cosine Functions

7-7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

7-8 Phase Shift; Sinusoidal Curve Fitting

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

8. Analytic Trigonometry

8-1 The Inverse Sine, Cosine, and Tangent Functions

8-2 The Inverse Trigonometric Functions (Continued)

8-3 Trigonometric Equations

8-4 Trigonometric Identities

8-5 Sum and Difference Formulas

8-6 Double-angle and Half-angle Formulas

8-7 Product-to-Sum and Sum-to-Product Formulas

9. Applications of Trigonometric Functions

9-1 Applications Involving Right Triangles

9-2 The Law of Sines

9-3 The Law of Cosines

9-4 Area of a Triangle

9-5 Simple Harmonic Motion; Damped Motion; Combining Waves

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

10. Polar Coordinates; Vectors

10-1 Polar Coordinates

10-2 Polar Equations and Graphs

10-3 The Complex Plane, De Moivre’s Theorem

10-4 Vectors

10-5 The Dot Product

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

11. Analytic Geometry

11-1 Conics

11-2 The Parabola

11-3 The Ellipse

11-4 The Hyperbola

11-5 Rotation of Axes

11-6 Polar Equations of Conics

11-7 Plane Curves and Parametric Equations

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

12. Systems of Equations and Inequalities

12-1 Systems of Linear Equations: Substitutions and Elimination

12-2 Systems of Linear Equations: Matrices

12-3 Systems of Linear Equations: Determinants

12-4 Matric Algebra

12-5 Partial Fraction Decomposition

12-6 Systems of Nonlinear Equations

12-7 Systems of Inequalities

12-8 Linear Programming

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

13. Sequences; Induction; the Binomial Theorem

13-1 Sequences

13-2 Arithmetic Sequences

13-3 Geometric Sequences; Geometric Series

13-4 Mathematical Induciton

13-5 The Binomial Theorem

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

14. Counting and Probability

14-1 Counting

14-2 Permutations and Combinations

14-3 Probability

Chapter Review

Chapter Test

Cumulative Review

Chapter Projects

Answers

Credits

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