# Precalculus, 12th edition

Published by Pearson (April 26, 2024) © 2025

**Michael Sullivan**Chicago State University

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## MyLab

- Reach every student with personalized support
- Customize courses with ease
- Optimize learning with dynamic study tools

For courses in Precalculus.

### Support all students, at every level, in their mathematics journey

**Precalculus** features the high-quality exercises that distinguish Sullivan texts, with Sullivan’s proven cycle of continuous preparation and retention: *prepare* for class, *practice* with homework, and *review* concepts. It contains 1 review chapter before covering the traditional topics of polynomial, rational, exponential, and logarithmic functions and their graphs. The trigonometric functions are introduced using a unit circle approach, showing how it relates to the right triangle approach. Graphing technology (TI-84 Plus CE and Desmos) is provided and optional.

The **12th Edition** adds many new and revised exercises and examples; adds new learning tips in margin notes; updates all graphing utility content and images; and much more.

### Hallmark features of this title

**Preparing for This Section**lists earlier concepts that will be useful in the section ahead, with page references.**All examples are clearly written**and most conclude with a direction to**Now Work,**a related exercise, helping students to learn by doing.**Showcase Examples**offer a guided, step-by-step approach to solving a problem; highlighted**Model It**examples and exercises ask students to build a mathematical model from verbal descriptions or from data.**Now Work**and**Are You Prepared? problems**help students see if they are ready to proceed to the section ahead.**Calculus icons**appear next to information essential for the study of calculus.**In Words**translates math into plain English.

### New and updated features of this title

**New and revised graphing utility screen captures**include more Desmos and TI-84 Plus images to provide alternate ways of visualizing concepts and making connections between equations, data, and graphs in full color.- Makes use of Desmos to simplify finding points of interest such as local extrema, intercepts, and points of intersection with systems of equations, and is a powerful tool for graphing implicit equations and polar curves.

**New and revised margin notes**are provided where appropriate:**Need To Review?**are a timely reference to the chapter, section and page where a student may need to refresh a particular skill needed for the material.**In Words**notes help students focus on the concept of a given formula, definition or theorem. Occasional**Note**features further clarify reasoning or make connections to prior concepts.**Seeing the Concept**features appear strategically where graphing exploration may help strengthen understanding.**Career Tips**and**Fun Facts**help students connect the topic at hand to the world around them.**Caution**notes help students avoid common mistakes.

**New, inspirational Contemporary Mathematicians highlights**appear near the start of each chapter. This selection of diverse mathematicians and scientists who have made advancements in various fields explores “who is a mathematician? What are they working on, and what was their journey?”

### Features of MyLab Math for the 12th Edition

**New and revised Exercises:**All exercises have been reviewed and revised by Michael Sullivan III to better reflect the pedagogical intent of each.- Expands the number of questions students must complete within each problem, to better develop conceptual understanding and improve the graphing exercises.
- Significantly improves the guidance within the learning aids to reflect the approach of the text and to provide more detailed instruction.

**New instructional videos:**Created exclusively for this MyLab course, all videos were entirely reviewed by the author, with Michael Sullivan III appearing in many along with a variety of other instructors. There is 1 video for each objective in the book, and each is divided into shorter Introductions, Examples, and Summary for ease of use. Additional video features include:**Interactive Figures**to help students visualize key concepts;**handwriting**to accommodate students who prefer seeing examples worked out by hand**High-definition****resolution**to make the videos clearly readable on phones;**accessible**with close-captioning.

### 1. Graphs

- 1.1 The Distance and Midpoint Formulas
- 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
- 1.3 Lines
- 1.4 Circles
- Chapter 1 Review, Test, and Projects

### 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 2 Review, Test, and 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 3 Review, Test, and Projects

### 4. Polynomial and Rational Functions

- 4.1 Polynomial Functions
- 4.2 Graphing Polynomial Functions; Models
- 4.3 Properties of Rational Functions
- 4.4 The Graph of a Rational Function
- 4.5 Polynomial and Rational Inequalities
- 4.6 The Real Zeros of a Polynomial Function
- Chapter 4 Review, Test, and 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 5 Review, Test, and 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 6 Review, Test, and 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 7 Review, Test, and 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 8 Review, Test, and Projects

### 9. Polar Coordinates; Vectors

- 9.1 Polar Coordinates
- 9.2 Polar Equations and Graphs
- 9.3 The Complex Plane; De Moivre's Theorem
- 9.4 Vectors
- 9.5 The Dot Product
- 9.6 Vectors in Space
- 9.7 The Cross Product
- Chapter 9 Review, Test, and 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 10 Review, Test, and 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 11 Review, Test, and 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 12 Review, Test, and Projects

### 13. Counting and Probability

- 13.1 Counting
- 13.2 Permutations and Combinations
- 13.3 Probability
- Chapter 13 Review, Test, and Projects

### 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
- 14.5 The Area Problem; The Integral
- Chapter 14 Review, Test, and Projects

### Appendix A: 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
*n*th Roots; Rational Exponents

### Appendix B: Graphing Utilities

- B.1 The Viewing Rectangle
- B.2 Using a Graphing Utility to Graph Equations
- B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
- B.4 Using a Graphing Utility to Solve Equations
- B.5 Square Screens
- B.6 Using a Graphing Utility to Graph Inequalities
- B.7 Using a Graphing Utility to Solve Systems of Linear Equations
- B.8 Using a Graphing Utility to Graph a Polar Equation
- B.9 Using a Graphing Utility to Graph Parametric Equations

#### Answers

#### Credits

#### Index

### About our author

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.

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