Precalculus, 12th Edition © 2025
Michael Sullivan
Precalculus, 12th Edition 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.
- 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?”
- 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.
- 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 nth 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
Michael Sullivan
Chicago State University
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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| Format | ISBN-13 |
|---|---|
| Student edition | 9780138305567 |
| Student edition + MyMathLab for School with Pearson eTextbook (1-year access) | 9780138305512 |
| Student edition + MyMathLab for School with Pearson eTextbook (6-year access) | 9780138305529 |
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| Annotated teacher's edition | 9780138279066 |
| MyMathLab for School with Pearson eTextbook (1-year access) | 100% digital solution. Access code is delivered via email. | 9780132962377 |
| MyMathLab for School with Pearson eTextbook (6-year access) | 100% digital solution. Access code is delivered via email. | 9780132962391 |
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