Precalculus: Enhanced with Graphing Utilities, 9th edition

Published by Pearson (November 19, 2024) © 2026

  • Michael Sullivan Chicago State University
  • Michael Sullivan Joliet Junior College

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For courses in Precalculus.

Adapts to contemporary students’ varying needs

The proven approach of Sullivan and Sullivan focuses students on the fundamental skills of the course: prepare for class, practice with homework, and review the concepts.  Precalculus: Enhanced with Graphing Utilities fully integrates graphing utilities into topics, allowing students to explore mathematical concepts and encounter ideas usually studied in later courses. Many examples show solutions using algebra side by side with graphing techniques. The text features a review chapter before covering the traditional precalculus topics of functions and their graphs, polynomial and rational functions, and exponential and logarithmic functions. The trigonometric functions are introduced using a unit circle approach and show how it is related to the right triangle approach.

The 9th Edition is revised and refined throughout, with updated Desmos and screen captures as well as TI-84 Plus CE screens; updates exercise sets with timely and relevant scenarios; adds a new Highlighting Contemporary Mathematicians feature, and much more.

Hallmark features of this title 

  • Just-in-time review begins all sections to prepare students for the topics ahead, with Preparing for This Section lists and Are You Prepared?  Problems.
  • Section-level guidance helps develop problem-solving skills with Showcase Examples, highlighted Model It examples, Model It exercises, Now Work problems after most examples, Calculus icons and much more.
  • Challenge Problems are thought provoking and require some ingenuity to solve. They can be used individually or for group work.
  • Assess Your Understanding appears after every section with a variety of problems for students to master needed skills.
  • Chapter Reviews offer a variety of convenient tools for reference and review, including You Should be Able To… objective lists and exercises by section; Review Exercises matched to learning objectives; Chapter Tests containing 15-20 problems each; and Cumulative Review problem sets.

New and updated features of this title

  • NEW: Highlighting Contemporary Mathematicians begin each chapter. These short bios present a selection of diverse contemporary mathematicians and scientists making advancements in various fields, demonstrating math at work in our world and inspiring students to pursue their own mathematical and scientific journeys.
  • NEW/REVISED: More Desmos and screen captures along with TI-84 Plus CE screen captures have been added throughout. These provide alternate ways of visualizing concepts and making connections between equations, data, and graphs in full color.
  • NEW/REVISED: All exercise sets have been reviewed and analyzed, with many replaced or updated as needed. All time-sensitive problems, especially those involving data, have been updated to the most recent information available.
    • Exercises have been updated with current and relevant scenarios such as credit card debt and revenue earned by social media influencers; financial planning exercises utilize dollar amounts more realistic for current students.
  • REVISED: Updated Applications and Extensions problems throughout also include many new application-type exercises, many of which involve data drawn from sources the student will recognize, to improve relevance and timeliness.
  • NEW: Key to Exercise Types helps users navigate the features of the exercise sets, using a key at the bottom of the first page for each section’s exercises. Categories include Now Work, Modeling, Explaining Concepts, Calculus Preview, and Interactive Figure.

Features of MyLab Math for the 9th Edition

  • NEW: Every instructional video is new and created exclusively for this text. They are author reviewed and Michael Sullivan III appears in many. Videos are objective based, with 1 for each textbook objective, and segmented into shorter parts for easier navigation (Introductions, Examples, and Summary). Interactive Figures help students visualize key concepts, and show examples worked by hand. Each video is high-definition and accessible, and various instructors appear across the selection.
  • NEW: GeoGebra Graphing Exercises are gradable graphing exercises that help students demonstrate their understanding. They enable students to interact directly with the graph in a manner that reflects how they would graph on paper.
  • NEW section-level Enhanced Assignments:
    • help keep skills fresh with spaced practice of previously learned concepts. The spaced practice problems are selected from the Retain Your Knowledge problems in the textbook.
    • turn off learning aids strategically for some exercises to ensure that students understand how to work the exercises independently.
    • contain personalized prerquisite skills exercises for gaps identified in the chapter-level Skills Check Quiz.
  • NEW: Video Note-Taking Guide helps students learn actively while watching videos.
  • UPDATED: All MyLab exercises have been reviewed and edited to better match the language and approach of the text, and to make solutions (within View an Example and Help Me Solve This) more student friendly.

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, Arc Length, and Circular Motion
  • 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; 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 Investigating Limits Using Tables and Graphs
  • 14.2 Algebraic Techniques for Finding Limits
  • 14.3 One-sided Limits; Continuity
  • 14.4 The Tangent Problem; The Derivative
  • 14.5 The Area Problem; The Integral
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

Appendix: Review

  • A.1 Algebra Essentials
  • A.2 Geometry Essentials
  • A.3 Polynomials
  • A.4 Synthetic Division
  • A.5 Rational Expressions
  • 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

Answers

Credits

Subject Index

About our authors

After graduating from Saint Ignatius College Prep (Chicago), Michael Sullivan attended DePaul University as an undergraduate, completing a major in mathematics and a minor in physics in 3 years. He pursued his graduate studies at the Illinois Institute of Technology, receiving a master's degree in 1963 and a Doctor of Philosophy (PhD) in 1967, both in mathematics.

Mike had a teaching career of over 30 years at Chicago State University as a Professor of Mathematics, where he honed an approach to teaching and writing that forms the foundation for his textbooks. He has authored more than 120 textbooks in mathematics and currently has 15 books in print. His textbooks are used in high schools and universities across the United States and have been translated into a variety of foreign languages. His books have been awarded both the Texty and McGuffey awards from the Textbook and Academic Authors Association (TAA), and in 2007 he received the TAA Lifetime Achievement Award. In 2023, Mike was awarded the Saint Ignatius College Prep Alumni Award for Excellence, in recognition of his outstanding commitment to his profession and to the Saint Ignatius community.

Mike is a member of the American Mathematical Association of Two-Year Colleges, the American Mathematical Society, the Mathematical Association of America, and the Textbook and Academic Authors Association. He has 4 children, all of whom are involved with mathematics or publishing. His son, Michael Sullivan III, also teaches college mathematics and is his coauthor on 2 Pearson precalculus series.  He divides his time between living in Naples, FL and Oak Lawn, IL. When not writing textbooks he enjoys tennis, travel and gardening.

Michael Sullivan, III is an adjunct professor of Mathematics at Florida SouthWestern State College. He took this position after retiring from Joliet Junior College (the nation’s oldest public community college). He taught at Joliet Junior College for 25 years. Prior to teaching at Joliet Junior College, Michael taught high school mathematics. He holds graduate degrees from DePaul University in both mathematics and economics.

Michael has been actively presenting at both national and regional conferences for over 25 years. He currently has a Statistics series in its 7th edition and a Developmental Mathematics series in its 4th edition. He also writes a Precalculus series with his father.

Michael’s interests in the classroom lie in developing exciting and innovative techniques for delivering course content to help keep his students engaged. He strongly believes in developing students’ communication skills (both written and oral) and developing students' conceptual understanding of mathematics. His experience in course redesign, corequisites, and writing texts for the college-level math and statistics courses gives him a unique insight into what students need to be successful.

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