# Precalculus, 11th edition

Published by Pearson (April 26, 2019) © 2020

**Michael Sullivan**Chicago State University

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## MyLab

- Reach every student with personalized support
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For courses in Precalculus.

### Prepare. Practice. Review.

Michael Sullivan's time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. **Precalculus, 11th Edition **continues to evolve to meet the needs of today's students. The Sullivan series of texts prepares and supports students with access to help, where and when they require it. The hallmark Sullivan cycle of **continuous preparation and retention, **and the high-quality exercises that Sullivan texts are known for, give students the reinforcement they need.

### 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 "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.**Warnings**point out common mistakes and help students avoid them.

### New and updated features of this title

**Need to Review?**is now placed at the point of need for students. It provides a reference and page number to the discussion of a previous topic used in the current presentation.**Graphing Images**throughout each chapter show TI-84 Plus C and Desmos screenshots. Using the graphing technology students are most familiar with, these images help students visualize concepts clearly and make stronger connections among equations, data and graphs in full color.**Updated Guided Lecture Notes**ask students to complete definitions, procedures, and examples based on the content of the Author in Action videos and book. By directing students into essential material, students can focus and retain the most important concepts.**Updated and expanded exercise sets**appear throughout.**Updated Applications and Extensions**reflect the most current data available.**Retain Your Knowledge exercises**improve students' recall of concepts learned earlier in the course. The 11th Edition includes additional exercises that emphasize content students will build upon in the immediate upcoming section.**Challenge Problems**now appear in most Exercise sets at the end of Applications and Extensions. They are thought-provoking and require some ingenuity to solve. They can be used for group work or individually.

### Features of MyLab Math for the 11th Edition

**Integrated Review is now included**for corequisite courses or simply to help students who enter without a full understanding of prerequisite skills and concepts. Integrated Review provides videos on review topics with a corresponding worksheets, along with premade, assignable skills-check quizzes and personalized review homework assignments.**Algebra Review**offers 4 chapters of Intermediate Algebra that are ideal for a corequisite or a slower-paced course. Videos can be assigned to accompany the Algebra Review content.**New Mindset material**encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as learning opportunities.**New****Guided Visualizations**, powered by GeoGebra and created by the author, help students visualize concepts through directed exploration and purposeful manipulation.**The new****College Algebra Essential Video Series**covers essential topics; videos can be assigned in a homework assignment to remind students of the crucial content before they begin on their exercises.**Enhanced Sample Assignments**use a thoughtful mix of Sullivan hallmark practice problems that are geared to maximize students' performance.**New Student & Assignment Tagging functionality**makes it easier for instructors to manage their courses.

### 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 authors

**Mike Sullivan **recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago's South Side and currently resides in Oak Lawn, Illinois. Mike has 4 children; the 2 oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son Mike Sullivan, III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than 10 books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where he enjoys gardening.

**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 3 children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.

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