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
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Precalculus Program with Digital Integration

Precalculus prepares students for future success with a fundamental approach and contemporary tools.

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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 in-class 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.

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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? Problems
    Are 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? Reminders
    New 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 Examples
    Showcase Examples provide how-to instruction by offering a guided, step-by-step approach to solving a problem. Students can immediately see how each of the steps in a problem is employed.
  • Model It Examples
    Model 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 Problems
    Now Work problems follow most examples and point to a related exercise for immediate reinforcement of the skill or concept.
  • Calculus Icons
    Calculus 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.
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  • Guided Lecture Notes
    Updated 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 Captures
    Desmos and TI-84 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 Projects
    New and Revised Chapter Projects give students an up-to-the-minute experience. Many of the new projects require students to research information online in order to solve problems.
  • Concepts and Vocabulary Questions
    Fill-in-the-blank 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 Problems
    Mixed 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 Extensions
    Applications and Extensions allow students to apply their skills to real-world problems and to extend concepts learned in the section. These exercises have been updated and many new problems have been added.
  • Challenge Problems
    New Challenge Problems now appear in the Applications and Extensions part of the section exercises for students seeking problems with greater rigor.
  • Interactive Figure Exercises
    New Interactive Figure Exercises require students to manipulate an interactive figure to solve. These exercises are marked by a special icon.
  • Explaining Concepts Problems
    Explaining 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 Problems
    Revised and Expanded Retain your Knowledge problems maintain students’ skills or prepare them for upcoming sections or future calculus classes.
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  • 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 Exercises
    Review Exercises provide comprehensive coverage and practice of key skills matched to the Learning Objectives for each section.
  • Chapter Tests
    Chapter Tests contain 15-20 problems that can help students prepare for in-class 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 Sets
    Cumulative Review problem sets appear at the end of every chapter after Chapter 1.
  • Essential Video Series
    The 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.
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  • Sample Assignments
    Enhanced Sample Assignments are pre-made section-level assignments that address key concepts within the section and help keep previously learned skills fresh with Retain your Knowledge questions.
  • Setup & Solve Exercises
    New 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 Exercises
    Concept and Vocabulary exercises are now assignable as reading quizzes.
  • Skills Check Quizzes
    Skills Check Quizzes by chapter assess the prerequisite skills students need for that chapter.
  • Personalized Skills Review
    Personalized 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 Materials
    New Mindset materials encourage students to maintain a positive attitude about learning, value their ability to grow, and view mistakes as learning opportunities.
  • Interactive Figures
    New 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 Videos
    Author in Action Videos are actual classroom lectures with fully worked-out examples presented by Michael Sullivan III. Video assessment questions are available to assign for key videos.
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Empower Your Math Students with the MyMathLab® Platform from Pearson

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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 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.

  • 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 Project

    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

    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

    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    4. 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 Projects

    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

    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    6. 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 Projects

    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

    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    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

    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    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

    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

    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

    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

    13. Counting and Probability

    • 13.1 Counting
    • 13.2 Permutations and Combinations
    • 13.3 Probability

    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    14. 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 One-sided Limits; Continuous Functions
    • 14.4 The Tangent Problem; The Derivative
    • 14.5 The Area Problem; The Integral

    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    Appendix 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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