# Precalculus Enhanced with Graphing Utilities, 8th edition

Published by Pearson (April 30, 2020) © 2021

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

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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.

### Prepare, practice, review

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. In the **8th Edition, **all exercises and examples in the text have been reviewed and updated as needed, and the authors have added new problem-solving and review features.

**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.**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:**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

**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.**Graphing Utility Screen Captures**: Desmos screen captures have been added in several instances, along with the TI-84 Plus CE screen captures. These updated screen captures provide alternative ways of visualizing concepts and making connections between equations, data, and graphs in full color.**New and enhanced 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.**Expanded Retain Your Knowledge**problems: in most sections, problems preview skills students need to succeed in subsequent sections or in calculus (identified by a calculus icon). All answers to Retain Your Knowledge problems are in the back of the text and these problems are included in pre-built Enhanced Sample Assignments.**Challenge Problems**now appear in the Applications and Extensions part of the section exercises, for students seeking problems with greater rigor.**Key to Exercise Types**helps users navigate the features of the exercise sets with a key at the bottom of the first page of each section's exercises.

### Features of MyLab Math for the 8th Edition

**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**require students to show how they set up a problem as well as the solution. Both traditional and Setup & Solve versions of exercises within MyLab are provided.**Integrated Review**content and assessments give students just the remediation they need, including**Skills Check Quizzes**by chapter;**Personalized Skills Review Homework**generated for each student based on the results of the Skills Check Quiz;**Algebra Review eText, Exercises, Videos and Worksheets**for additional help or for co-requisite courses.**Interactive Figures**(formerly Guided Visualizations) are expanded to support teaching and learning. Created in GeoGebra by author Michael Sullivan III, the figures illustrate key concepts and allow manipulation. They have been designed to be used in lectures as well as by students independently.**Personal Inventory Assessments**are a collection of online exercises designed to promote self-reflection and engagement in students. These 33 assessments include topics such as a Stress Management Assessment and Time Management Assessment.

### 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
*n*th Roots; Rational Exponents

### Appendix B: The Limit of a Sequence; Infinite Series

#### Answers

#### Credits

#### Subject Index

### About our authors

**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 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 4 children: Kathleen teaches college mathematics; Michael III teaches college mathematics and is his co-author on 2 precalculus series; Dan works in publishing; and Colleen teaches middle school and secondary school mathematics. Twelve grandchildren round out the family.

**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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