# Precalculus: Functions and Graphs, 4th edition

Published by Pearson (December 27, 2011) © 2013

**Mark Dugopolski**Southeastern Louisiana University

## eTextbook

- Easy-to-use search and navigation
- Add notes and highlights
- Flashcards help streamline study sessions

*For courses in Precalculus.*

**The Right Tools to Drive Your Success**

Dugopolski’s **Precalculus: Functions and Graphs, Fourth Edition** gives students the essential strategies they need to make the transition to calculus. Along the way, students see how the algebra connects to their future calculus courses, with tools like Foreshadowing Calculus and Concepts of Calculus. The author’s emphasis on problem solving and critical thinking is enhanced by a new **MyMathLab** course, where students will find new *Video Assessment* questions tied to section lecture videos; *Getting Ready* material to help learn necessary prerequisite skills; *Guided Visualizations,* and more!

**Also available with MyMathLab**

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

*This Media Update features an enhanced MyMathLab course. This © 2017 version of the textbook is completely compatible with the earlier © 2013 version.*

**About the Book**

**Strategies for success:**Learning aids are strategically placed to give students guidance when they need it.

**Function Galleries**are designed to help students link the visual aspects of various families of functions to the properties of the functions. These appear throughout the text and are also gathered together at the beginning of the text.**Art Annotations**make the mathematical art a better learning tool and easier to use.**Summaries**of important concepts are included to help students clarify ideas that have multiple parts.**Strategies**show general guidelines for accomplishing tasks. Students can use them to sharpen problem-solving skills.**Procedures**are similar to*Strategies,*but are more specific and more algorithmic. They have also been highlighted in this edition and are designed to give students a step-by-step approach.**Foreshadowing Calculus**gives a brief indication of the connection between certain algebraic topics and calculus, and identifies topics that will be continued in calculus.**Concepts of Calculus discussions**conclude most chapters, and provide exercises designed to illustrate a specific concept. This full page feature gives students a preview of important topics of calculus, and may be used as a writing or collaborative learning assignment.**Chapter Openers**begin with discussion of a real-world situation that uses mathematics from the chapter. Examples and exercises that relate back to the opener are included in the chapter.- Optional
**Graphing Calculator Discussions**appear throughout the text. These are marked by graphing calculator icons so that they can be easily skipped if desired. Students who do not use a graphing calculator can still benefit from the technology discussions, as well as from the calculator-generated graphs that occur in the text. The author treats the graphing calculator as a tool to support and enhance algebraic conclusions, not to make conclusions. **Historical Notes**: located in the margins throughout the text, these brief essays are designed to connect the topics of precalculus to the mathematicians who first studied them and to give precalculus a human face.

**Milestones along the way:**Section exercise sets are rich and varied, giving students many opportunities to practice the skills they will need to succeed in this course and in their future calculus course.

**For Thought:**each exercise set is preceded by a set of ten true/false questions that review the basic concepts in the section, help check student understanding before beginning the exercises, and offer opportunities for writing and discussion. Assignable in MyMathLab, the answers to all For Thought exercises are included in the back of the student edition.**Fill-in-the-blank exercises**now appear at the beginning of the section exercise sets to help students learn definitions, rules, and theorems**.**These can be used for reading comprehension and are assignable in MyMathLab.**Writing/Discussion and Cooperative Learning Exercises**deepen students’ understanding by giving them the opportunity to express mathematical ideas both in writing and to their classmates during small group or team discussions.**Linking Concepts**exercises,at the end of nearly every exercise set, are multi-part exercises and explorations that can be used for individual or group work. These encourage students to use concepts from the current section along with concepts from preceding sections (or chapters) to solve problems that illustrate the links among various concepts. Some parts of these questions are open-ended and require more thought than standard skill-building exercises.**Thinking Outside the Box**problems throughout the text are designed to get students (and instructors) to do some mathematics just for fun. The problems can be used for individual or group work.**End-of-chapter material**helps students review and synthesize mathematical concepts as they prepare for the road ahead.

**NEW! Cumulative Review Exercises**now appear at the end of the section exercise sets to review the skills learned in previous sections and chapters. These exercises are under the heading “Rethinking” and are assignable in MyMathLab.

**Highlights**at the end of every chapter contain an overview of all of the concepts presented in the chapter along with brief examples to illustrate the concept.**Chapter Review exercises**are designed to give students a comprehensive review of the chapter and prepare students for the chapter test.**Chapter Tests**measure the students' readiness for a typical one-hour classroom test. Instructors may also use them as a model for their own end-of-chapter tests.**Tying It All Together exercises**at the end of most chapters help students review selected concepts from the present and prior chapters and require students to integrate multiple concepts and skills. These exercises are assignable in MyMathLab.

**Instructor-friendly tools**save time before and during class.

**Pop Quizzes**are included in every section. These give instructors convenient 8- to 10-question quizzes that can be used in the classroom to confirm comprehension of the basics. Answers are located in the Annotated Instructor’s Edition.**Example Numbers**appear at the end of the direction line for nearly all groups of exercises, indicating which examples correspond to the exercises. These appear in the Annotated Instructor’s Edition, and make it easier to assign homework problems.

**Also available with MyMathLab**

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

*This Media Update features an enhanced MyMathLab course. This © 2017 version of the textbook is completely compatible with the earlier © 2013 version.*

**NEW!**With**Getting Ready**content, students refresh prerequisite topics through assignable skill-review quizzes and personalized homework.**NEW! The Video Notebook**is a printed guide that gives students a structured place to take notes as they watch the videos. Definitions, examples, and important concepts are highlighted, and helpful hints are pointed out along the way. The notebook is available in MyMathLab.**NEW! Video assessment**is tied to the video lecture for each section of the book to check students’ conceptual understanding of important math concepts. Instructors can assign these video questions seamlessly within a homework assignment. .**NEW! Guided Visualizations**bring mathematical concepts to life. These interactive, animated figures help students visualize the concepts through directed explorations and purposeful manipulation. These are assignable in MyMathLab and encourage active, conceptual learning and critical thinking. HTML5 format means no plug-ins required!**NEW! Skills for Success Modules**help students succeed in collegiate courses and prepare for future professions. Topics such as “Time Management,” “Stress Management,” and “Financial Literacy” are available for you to assign to your students.**NEW! Graphing Calculator manual**is organized to follow the sequence of topics in the text, and provides an easy-to-follow, step-by-step guide with worked-out examples to help students fully understand and get the most out of their graphing calculator. Compatible models include the popular TI-83/84 Plus and TI-89.

**About the Book**

**Milestones along the way:**Section exercise sets are rich and varied, giving students many opportunities to practice the skills they will need to succeed in this course and in their future calculus course.

**Fill-in-the-blank exercises**now appear at the beginning of the section exercise sets to help students learn definitions, rules, and theorems**.**These can be used for reading comprehension and are assignable in MyMathLab.

**Cumulative Review Exercises**now appear at the end of the section exercise sets to review the skills learned in previous sections and chapters. These exercises are under the heading “Rethinking” and are assignable in MyMathLab.

**Highlights**at the end of every chapter contain an overview of all of the concepts presented in the chapter along with brief examples to illustrate the concept.**Chapter Review exercises**are designed to give students a comprehensive review of the chapter and prepare students for the chapter test.**Chapter Tests**measure the students' readiness for a typical one-hour classroom test. Instructors may also use them as a model for their own end-of-chapter tests.**Tying It All Together exercises**at the end of most chapters help students review selected concepts from the present and prior chapters and require students to integrate multiple concepts and skills. These exercises are assignable in MyMathLab.

**Also available with MyMathLab**MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a

*This Media Update features an enhanced MyMathLab course. This © 2017 version of the textbook is completely compatible with the earlier © 2013 version.*

- With
**Getting Ready**content, students refresh prerequisite topics through assignable skill-review quizzes and personalized homework. **The Video Notebook**is a printed guide that gives students a structured place to take notes as they watch the videos. Definitions, examples, and important concepts are highlighted, and helpful hints are pointed out along the way. The notebook is available in MyMathLab.**Video assessment**is tied to the video lecture for each section of the book to check students’ conceptual understanding of important math concepts. Instructors can assign these video questions seamlessly within a homework assignment. .**Guided Visualizations**bring mathematical concepts to life. These interactive, animated figures help students visualize the concepts through directed explorations and purposeful manipulation. These are assignable in MyMathLab and encourage active, conceptual learning and critical thinking. HTML5 format means no plug-ins required!**Skills for Success Modules**help students succeed in collegiate courses and prepare for future professions. Topics such as “Time Management,” “Stress Management,” and “Financial Literacy” are available for you to assign to your students.**Graphing Calculator manual**is organized to follow the sequence of topics in the text, and provides an easy-to-follow, step-by-step guide with worked-out examples to help students fully understand and get the most out of their graphing calculator. Compatible models include the popular TI-83/84 Plus and TI-89.

## Table of Contents

**Equations, Inequalities, and Modeling**- 1-1 Equations in One Variable
- 1-2 Constructing Models to Solve Problems
- 1-3 Equations and Graphs in Two Variables
- 1-4 Linear Equations in Two Variables
- 1-5 Scatter Diagrams and Curve Fitting
- 1-6 Complex Numbers
- 1-7 Quadratic Equations
- 1-8 Linear and Absolute Value Inequalities

- Chapter 1 Highlights
- Chapter 1 Review Exercises
- Chapter 1 Test
- Concepts of Calculus: Limits

**Functions and Graphs**- 2-1 Functions
- 2-2 Graphs of Relations and Functions
- 2-3 Families of Functions, Transformations, and Symmetry
- 2-4 Operations with Functions
- 2-5 Inverse Functions
- 2-6 Constructing Functions with Variation

- Chapter 2 Highlights
- Chapter 2 Review Exercises
- Chapter 2 Test
- Tying it all Together
- Concepts of Calculus: Instantaneous Rate of Change

**Polynomial and Rational Functions**- 3-1 Quadratic Functions and Inequalities
- 3-2 Zeroes of Polynomial Functions
- 3-3 The Theory of Equations
- 3-4 Miscellaneous Equations
- 3-5 Graphs of Polynomial Functions
- 3-6 Rational Functions and Inequalities

- Chapter 3 Highlights
- Chapter 3 Review Exercises
- Chapter 3 Test
- Tying it all Together
- Concepts of Calculus: Instantaneous Rate of Change of the Power Functions

**Exponential and Logarithmic Functions**- 4-1 Exponential Functions and Their Applications
- 4-2 Logarithmic Functions and Their Applications
- 4-3 Rules of Logarithms
- 4-4 More Equations and Applications

- Chapter 4 Highlights
- Chapter 4 Review Exercises
- Chapter 4 Test
- Tying it all Together
- Concepts of Calculus: The Instantaneous Rate of Change of f(x)= ex

**The Trigonometric Functions**- 5-1 Angles and Their Measurements
- 5-2 The Sine and Cosine Functions
- 5-3 The Graphs of the Sine and Cosine Functions
- 5-4 The Other Trigonometric Functions and Their Graphs
- 5-5 The Inverse Trigonometric Functions
- 5-6 Right Triangle Trigonometry

- Chapter 5 Highlights
- Chapter 5 Review Exercises
- Chapter 5 Test
- Tying it all Together
- Concepts of Calculus: Evaluating Transcendental Functions

**Trigonometric Identities and Conditional Equations**- 6-1 Basic Identities
- 6-2 Verifying Identities
- 6-3 Sum and Difference Identities
- 6-4 Double-Angle and Half-Angle Identities
- 6-5 Product and Sum Identities
- 6-6 Conditional Trigonometric Functions

- Chapter 6 Highlights
- Chapter 6 Review Exercises
- Chapter 6 Test
- Tying it all Together
- Concepts of Calculus: Area of A Circle and n

**Applications of Trigonometry**- 7-1 The Law of Sines
- 7-2 The Law of Cosines
- 7-3 Vectors
- 7-4 Trigonometric Form of Complex Numbers
- 7-5 Powers and Roots of Complex and Numbers
- 7-6 Polar Equations

- Chapter 7 Highlights
- Chapter 7 Review Exercises
- Chapter 7 Test
- Tying it all Together
- Concepts of Calculus: Limits and Asymptotes

**Systems of Equations and Inequalities**- 8-1 Systems of Linear Equations in Two Variables
- 8-2 Systems of Linear Equations in Three Variables
- 8-3 Nonlinear Systems of Inequalities
- 8-4 Partial Fractions
- 8-5 Inequalities and Systems of Inequalities in Two Variables
- 8-6 The Linear Programming Model

- Chapter 8 Highlights
- Chapter 8 Review Exercises
- Chapter 8 Test
- Tying it all Together
- Concepts of Calculus: Instantaneous Rate of Change and Partial Fractions

**Matrices and Determinants**- 9-1 Solving Linear Systems Using Matrices
- 9-2 Operations with Matrices
- 9-3 Multiplication of Matrices
- 9-4 Inverses of Matrices
- 9-5 Solution of Linear Systems in Two Variables Using Determinants
- 9-6 Solution of Linear Systems in Three Variables Using Determinants

- Chapter 9 Highlights
- Chapter 9 Review Exercises
- Chapter 9 Test
- Tying it all Together

**The Conic Series**- 10-1 The Parabola
- 10-2 The Ellipse and the Circle
- 10-3 The Hyperbola
- 10-4 Rotation of Axes
- 10-5 Polar Equations of the Conics

- Chapter 10 Highlights
- Chapter 10 Review Exercises
- Chapter 10 Test
- Tying it all Together
- Concepts of Calculus: The Reflection Property of a Parabola

**Sequences, Series, and Probability**- 11-1 Sequences
- 11-2 Series
- 11-3 Geometric Sequences and Series
- 11-4 Counting and Permutations
- 11-5 Combinations, Labeling, and the Binomial Theorem
- 11-6 Probability
- 11-7 Mathematical Induction

- Chapter 11 Highlights
- Chapter 11 Review Exercises
- Chapter 11 Test
- Concepts of Calculus: Limits of Sequences

### A. Appendix: Solutions to Try This Exercises

### B. Appendix: Basic Algebra Review

- B-1 Real Numbers and Their Properties
- B-2 Exponents and Radicals
- B-3 Polynomials
- B-4 Factorials Polynomials
- B-5 Rational Expressions

#### Credits

#### Answers to Selected Exercises

#### Index of Applications

#### Index

**Mark Dugopolski** was born in Menominee, Michigan. After receiving a B.S. from Michigan State University, he taught high school for four years, and then went on to receive an M.S. in mathematics from Northern Illinois University. He also received a Ph.D. in the area of topology from the University of Illinois at Champaign-Urbana. Mark has been teaching at Southeastern Louisiana in Hammond, LA, ever since. Mark has been writing textbooks for about fifteen years. He is married and has two daughters, and enjoys playing tennis, jogging, and riding his bicycle in his spare time.

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