Precalculus: Enhanced with Graphing Utilities, 8th Edition © 2021
In this edition of Precalculus, published by Pearson, all the exercises have been reviewed and updated. They stick with the Sullivans’ proven approach while allowing students to explore concepts and ideas they will encounter in later courses.
 Thorough integration of graphing utilities into topics
 Emphasis on visual and conceptual thinking
 Focus on fundamental skills
 Flexible and robust online toolkit
Precalculus Program with Digital Integration
Precalculus prepares students for future success with a fundamental approach and contemporary tools.
Prepare, Practice, Review
Precalculus’s lessons and homework are structured so students encounter concepts with some frequency. That way they deepen their understanding and draw connections.
Empowered Learning
Differentiation tools within the courseware help to identify students’ abilities. Teachers can build personalized skills reviews to make sure everyone is learning the material.
Technological Advantage
Teachers can reach students inclass or at home with a blended or 100% digital solution. Precalculus fully leverages the technology you have at our disposal.
Trusted Content
Now in its 8th edition, Precalculus continues to offer the high standards set by Michael Sullivan and Michael Sullivan III that have helped millions of students for over 15 years.
Precalculus Teaching Solutions

Preparing for Class

Practicing Skills

Chapter Reviews for Exams and Quizzes

Digital Support for Teachers and Students in MyMathLab for School

Are You Prepared? ProblemsAre You Prepared? Problems appear at the start of each exercise set. Students can check if they are ready to proceed to the section ahead or if they need to review earlier material further.

Need to Review? RemindersNew Need to Review? Reminders now appear in the margin for key review topics, pointing students to the location of the review material in the textbook.

Showcase ExamplesShowcase Examples provide howto instruction by offering a guided, stepbystep approach to solving a problem. Students can immediately see how each of the steps in a problem is employed.

Model It ExamplesModel It examples are now highlighted, making it easy to identify which examples help students learn to build a mathematical model from verbal descriptions or data.

Now Work ProblemsNow Work problems follow most examples and point to a related exercise for immediate reinforcement of the skill or concept.

Calculus IconsCalculus Icons appear next to information essential for the study of calculus. When the icon appears next to a definition, the notation used is consistent with that from calculus.

Guided Lecture NotesUpdated Guided Lecture Notes ask students to complete definitions, procedures, and examples based on the content of the Author in Action videos and text. By directing students into essential material, students can focus and retain the most important concepts.

Graphing Calculator Screen CapturesDesmos and TI84 Plus screen captures have been added in several instances. These updated images provide alternative ways of visualizing concepts and making connections between equations, data, and graphics.

Chapter ProjectsNew and Revised Chapter Projects give students an uptotheminute experience. Many of the new projects require students to research information online in order to solve problems.

Concepts and Vocabulary QuestionsFillintheblank and true/false Concepts and Vocabulary questions have been written to serve as reading quizzes. They can be assigned in MyMathLab for School.

Mixed Practice ProblemsMixed Practice problems offer comprehensive assessment of the skills learned in the section by asking questions that relate to more than one concept or objective. These problems may also require students to utilize skills learned in previous sections, helping them to see how concepts are tied together.

Applications and ExtensionsApplications and Extensions allow students to apply their skills to realworld problems and to extend concepts learned in the section. These exercises have been updated and many new problems have been added.

Challenge ProblemsNew Challenge Problems now appear in the Applications and Extensions part of the section exercises for students seeking problems with greater rigor.

Interactive Figure ExercisesNew Interactive Figure Exercises require students to manipulate an interactive figure to solve. These exercises are marked by a special icon.

Explaining Concepts ProblemsExplaining Concepts: Discussion and Writing problems are marked by red numbers. These support class discussion, verbalization of mathematical ideas, and writing and research projects.

Retain Your Knowledge ProblemsRevised and Expanded Retain your Knowledge problems maintain students’ skills or prepare them for upcoming sections or future calculus classes.

You Should Be Able To…You Should Be Able To… is a list of every objective, by section, with corresponding practice exercises. Doing the recommended exercises allows students to master the key concepts.

Review ExercisesReview Exercises provide comprehensive coverage and practice of key skills matched to the Learning Objectives for each section.

Chapter TestsChapter Tests contain 1520 problems that can help students prepare for inclass exams. For additional help, they can watch an instructor work out full solutions on the Chapter Test Prep Video in MyMathLab for School.

Cumulative Review Problem SetsCumulative Review problem sets appear at the end of every chapter after Chapter 1.

Essential Video SeriesThe new College Algebra Essential Video Series covers the essential topics a college algebra student needs to understand to be successful in this course. Videos can be assigned to remind students of crucial content before students begin on their exercises.

Sample AssignmentsEnhanced Sample Assignments are premade sectionlevel assignments that address key concepts within the section and help keep previously learned skills fresh with Retain your Knowledge questions.

Setup & Solve ExercisesNew Setup & Solve Exercises require students to show how they set up a problem as well as the solution to better reflect what is required on tests. The traditional versions of these exercises are also available to provide more options for assessing students.

Concept and Vocabulary ExercisesConcept and Vocabulary exercises are now assignable as reading quizzes.

Skills Check QuizzesSkills Check Quizzes by chapter assess the prerequisite skills students need for that chapter.

Personalized Skills ReviewPersonalized Skills Review Homework is generated for each student based on the results of the Skills Check Quiz to provide students with help to fill gaps in their prerequisite skills.

Mindset MaterialsNew Mindset materials encourage students to maintain a positive attitude about learning, value their ability to grow, and view mistakes as learning opportunities.

Interactive FiguresNew Interactive Figures have been expanded to support teaching and learning. The figures illustrate key concepts and allow manipulation. They can be used in class or for independent study.

Author in Action VideosAuthor in Action Videos are actual classroom lectures with fully workedout examples presented by Michael Sullivan III. Video assessment questions are available to assign for key videos.
Empower Your Math Students with the MyMathLab® Platform from Pearson
MyMathLab® for School from Pearson provides interactive resources for teachers and students working on functions, polynomials, and other Precalculus concepts.
More About Precalculus: Enhanced with Graphing Utilities

Michael Sullivan Author Bio
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. He 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

Michael Sullivan III Author Bio
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 coauthor 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.

Table of Contents
1. Graphs
 1.1 Graphing Utilities; Introduction to Graphing Equations
 1.2 The Distance and Midpoint Formulas
 1.3 Intercepts; Symmetry; Graphing Key Equations
 1.4 Solving Equations Using a Graphing Utility
 1.5 Lines
 1.6 Circles
Chapter Review
Chapter Test
Chapter Project2. Functions and Their Graphs
 2.1 Functions
 2.2 The Graph of a Function
 2.3 Properties of Functions
 2.4 Library of Functions; Piecewisedefined Functions
 2.5 Graphing Techniques: Transformations
 2.6 Mathematical Models: Building Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects3. 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
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects4. Polynomial and Rational Functions
 4.1 Polynomial Functions and Models
 4.2 The Graph of a Polynomial Function and Models
 4.3 The Real Zeros of a Polynomial Function
 4.4 Complex Zeros; Fundamental Theorem of Algebra
 4.5 Properties of Rational Functions
 4.6 The Graph of a Rational Function
 4.7 Polynomial and Rational Inequalities
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects5. Exponential and Logarithmic Functions
 5.1 Composite Functions
 5.2 OnetoOne 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
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects6. Trigonometric Functions
 6.1 Angles and Their Measure
 6.2 Trigonometric Functions: A 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
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects7. 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 Doubleangle and Halfangle Formulas
 7.7 ProducttoSum and SumtoProduct Formulas
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects8. 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
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects9. 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 Projects10. 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 Projects11. 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 Projects12. 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 Projects13. Counting and Probability
 13.1 Counting
 13.2 Permutations and Combinations
 13.3 Probability
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects14. A Preview of Calculus: The Limit, Derivative, and Integral of a Fraction
 14.1 Finding Limits Using Tables and Graphs
 14.2 Algebra Techniques for Finding Limits
 14.3 Onesided Limits; Continuous Functions
 14.4 The Tangent Problem; The Derivative
 14.5 The Area Problem; The Integral
Chapter Review
Chapter Test
Cumulative Review
Chapter ProjectsAppendix A: Review
 A.1 Algebra Essentials
 A.2 Geometry Essentials
 A.3 Polynomials
 A.4 Synthetic Division
 A.5 Rational Expressoins
 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: The Limit of a Sequence; Infinite Series
Answers
Credits
Subject Index
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