# Elementary and Intermediate Algebra: Graphs and Models, 5th edition

Published by Pearson (January 5, 2016) © 2017

**Marvin L. Bittinger**Indiana University Purdue University Indianapolis**David J. Ellenbogen**Community College of Vermont**Barbara L. Johnson**Indiana University Indianapolis

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*For courses in elementary and intermediate algebra.*

**Objective: Visualizing the Concepts**

One of the hallmarks of the Bittinger Developmental Math program is objective-based learning. In ** Elementary and Intermediate Algebra: Graphs and Models, Fifth Edition**, the authors place special emphasis on conceptual understanding, modeling, and visualization. Their goal is to help students “see the math” and learn algebra by making connections between the math and real-world applications. For the

**Fifth Edition**, the authors have made many updates to the text and applications, as well as to the accompanying resources. These include important enhancements to the MyMathLab course, new Active Learning Figures, and the creation of a new interactive video program, To-the-Point Objective Videos, associated with a new student workbook,

*MyMathGuide: Notes, Practice, and Video Path*.

**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. The text and MyMathLab course form a tightly integrated program with all new To-the-Point Objective Videos, Active Learning Figures, and *MyMathGuide* workbook.

**About the Book**

**A Visual Approach**

**NEW! Chapter Opener applications with Infographics**use current data and applications to present the math in context. These applications are linked to exercises in the text and MyMathLab course, as well as to other resources such as Active Learning Figures and Student Activities, to help students model, visualize, and learn the math.**Algebraic-Graphical Side-by-Side Solutions**give students a direct comparison between these two problem-solving methods. They demonstrate that there is more than one way to obtain a result and illustrate the comparative efficiency and accuracy of the two methods.**Visualizing the Graph**problem sets ask students to match equations and inequalities with their graphs. This helps students to recognize the important characteristics of the equation or inequality and to visualize the corresponding attributes of its graph. This feature is animated in**MyMathLab**^{®}, enabling the student to visualize concepts on an entirely new level.**Your Turns**offer calculator support at the point of use. These simple exercises are designed to provide students with immediate keystroke practice.

**Emphasis on Conceptual Understanding**

**NEW! Reading Checks**are designed for after reading the section, but before beginning the homework. Successful completion of a Reading Check indicates that the student is sufficiently prepared to work the section exercises. These are now also assignable in MyMathLab.**NEW! Student Activities**begin with real-world data and guide students to examine a key concept in each chapter, while analyzing the data and connecting other concepts. There is one activity per chapter and they are available in MyMathLab.**Try Exercise**icons, corresponding to nearly every example, point students to similar problems in the section exercise sets. By solving these problems, students can immediately reinforce their understanding of the mathematical concepts and skills presented in the examples. For easy identification in the exercise sets, the “Try” exercises have a shaded block on the exercise number. Answers to Try Exercises are given at the end of the exercise sets and in the back of the book.**Mid-Chapter Reviews**give students the opportunity to reinforce their understanding of the mathematical skills and concepts covered in the first half of the chapter, before moving on to new material.- Each Mid-Chapter Review begins with a
**Brief Summary**of the concepts studied in the first part of the chapter, often illustrated with a table or chart. **Guided Solutions**problems include fill-in blanks for students to complete specific steps that lead to the solution.**Mixed Review**exercises require an understanding of previously learned material to reinforce mastery of skills and concepts.**Problem-Solving Steps**, called out in the margins adjacent to selected Example Solutions, offer students at-a-glance reinforcement of the problem-solving process.**The end-of-section exercise sets include several special types of problems:****Concept Reinforcement Exercises**(also found in the chapter Study Summary) are True/False questions designed to increase understanding of the concepts, rather than merely assess students' skill at memorizing procedures.**“Aha!” Exercises**discourage rote learning and reward students who “look before they leap” into a problem. The “Aha!” designation is used the first time a new insight can be applied to a particular type of exercise and indicates to the student that there is a simpler way to complete the exercise with less computation.**TW (Thinking and Writing) Exercises**promote conceptual understanding and can also be used for class discussion and group projects.**Synthesis Exercises**help build critical-thinking skills by requiring students to use skills and concepts from the current section, along with those from previous sections. These are available in most exercise sets.- The
**Connecting the Concepts feature**helps students understand the “big picture,” by relating the concept at hand to previously learned and upcoming material.

**Additional Support**

**Collaborative Corner exercises,**appearing one to three times per chapter, are designed for group work.- The
**Study Summary**at the end of each chapter has been expanded to provide more comprehensive in-text practice and review.**Key Terms and Concepts**are paired with worked-out**Examples,**for reference and review, and with similar**Practice Exercises**for students.

**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.

**NEW! Active Learning Figures**are interactive animations that allow students to examine visual representations of concepts through both guided and open-ended exploration. These are linked to chapter openers andvother locations throughout the text and MyMathLab. Accompanying exercises provide additional practice and reinforcement.**NEW! Chapter Opener applications with Infographics**use current data and applications to present the math in context. These applications are linked to exercises in the text and MyMathLab course, as well as to Active Learning Figures and Student Activities, to help students model, visualize, and learn the math.**NEW! Student Activities**begin with real-world data and guide students to examine a key concept in each chapter, while analyzing the data and connecting other concepts. There is one activity per chapter and they are available in MyMathLab.is an objective-based workbook (available in print and in MyMathLab) for guided, hands-on learning. It offers vocabulary, skill, and concept review—along with problem-solving practice—with space for students to show their work and write notes. Students can follow along in*MyMathGuide: Notes, Practice, and Video Path**My MathGuide*while they watch the new To-the-Point Objective Videos, listen to their instructor lecture, or read the textbook.**NEW! Bittinger Video Program**includes all new To-the-Point Objective Videos—with new Graphing Calculator Video Tutorials—and Chapter Test Prep Videos.**Interactive “Your Turn” Exercises**in the videos prompt students to solve problems and receive instant feedback. The videos also can be used hand-in-hand with the new*MyMathGuide*workbook.**Graphing Calculator Video Tutorials**help students utilize the graphing calculator to solve exercises when appropriate. A graphing calculator emulator guides students through the steps of each solution in an easy-to-follow, visual format.

**New in the Book**

**Chapter Opener applications with Infographics**use current data and applications to present the math in context. These applications are linked to exercises in the text and MyMathLab course, as well as to other resources such as Active Learning Figures and Student Activities, to help students model, visualize, and learn the math.

**Reading Checks**are designed for after reading the section, but before beginning the homework. Successful completion of a Reading Check indicates that the student is sufficiently prepared to work the section exercises. These are now also assignable in MyMathLab.**Student Activities**begin with real-world data and guide students to examine a key concept in each chapter, while analyzing the data and connecting other concepts. There is one activity per chapter and they are available 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 personalized study plan that helps them absorb course material and understand difficult concepts. The text and MyMathLab course form a tightly integrated program with all new To-the-Point Objective Videos, Active Learning Figures, and *MyMathGuide* workbook.

**Active Learning Figures**are interactive animations that allow students to examine visual representations of concepts through both guided and open-ended exploration. These are linked to chapter openers andvother locations throughout the text and MyMathLab. Accompanying exercises provide additional practice and reinforcement.**Chapter Opener applications with Infographics**use current data and applications to present the math in context. These applications are linked to exercises in the text and MyMathLab course, as well as to Active Learning Figures and Student Activities, to help students model, visualize, and learn the math.**Student Activities**begin with real-world data and guide students to examine a key concept in each chapter, while analyzing the data and connecting other concepts. There is one activity per chapter and they are available in MyMathLab.**Bittinger Video Program**includes all new To-the-Point Objective Videos—with new Graphing Calculator Video Tutorials—and Chapter Test Prep Videos.**Interactive “Your Turn” Exercises**in the videos prompt students to solve problems and receive instant feedback. The videos also can be used hand-in-hand with the new*MyMathGuide*workbook.

**1. Introduction to Algebraic Expressions**

1.1 Introduction to Algebra

1.2 The Commutative, Associative, and Distributive Laws

1.3 Fraction Notation

1.4 Positive and Negative Real Numbers

Mid-Chapter Review

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponential Notation and Order of Operations

**2. Equations, Inequalities, and Problem Solving**

2.1 Solving Equations

2.2 Using the Principles Together

2.3 Formulas

Mid-Chapter Review

2.4 Applications with Percent

2.5 Problem Solving

2.6 Solving Inequalities

2.7 Solving Applications with Inequalities

**3. Introduction to Graphing and Functions**

3.1 Reading Graphs, Plotting Points, and Scaling Graphs

3.2 Graphing Equations

3.3 Linear Equations and Intercepts

3.4 Rates

3.5 Slope

Mid-Chapter Review

3.6 Slope-Intercept Form

3.7 Point-Slope Form; Introduction to Curve Fitting

3.8 Functions

**4. Systems of Equations in Two Variables**

4.1 Systems of Equations and Graphing

4.2 Systems of Equations and Substitution

4.3 Systems of Equations and Elimination

Mid-Chapter Review

4.4 More Applications Using Systems

4.5 Solving Equations by Graphing

**5. Polynomials**

5.1 Exponents and Their Properties

5.2 Negative Exponents and Scientific Notation

5.3 Polynomials and Polynomial Functions

5.4 Addition and Subtraction of Polynomials

5.5 Multiplication of Polynomials

5.6 Special Products

Mid-Chapter Review

5.7 Polynomials in Several Variables

5.8 Division of Polynomials

5.9 The Algebra of Functions

**6. Polynomial Factorizations and Equations**

6.1 Introduction to Polynomial Factorizations and Equations

6.2 Trinomials of the Type *x ^{2} + bx + c*

6.3 Trinomials of the Type *ax ^{2} + bx + c*

Mid-Chapter Review

6.4 Perfect-Square Trinomials and Differences of Squares

6.5 Sums or Differences of Cubes

6.6 Factoring: A General Strategy

6.7 Applications of Polynomial Equations

**7. Rational Expressions, Equations, and Functions**

7.1 Rational Expressions and Functions

7.2 Multiplication and Division

7.3 Addition, Subtraction, and Least Common Denominators

7.4 Addition and Subtractions with Unlike Denominators

Mid-Chapter Review

7.5 Complex Rational Expressions

7.6 Rational Equations

7.7 Applications Using Rational Equations and Proportions

7.8 Formulas, Applications, and Variation

**8. Inequalities**

8.1 Graphical Solutions and Compound

8.2 Absolute Value Equations and Inequalities

Mid-Chapter Review

8.3 Inequalities in Two Variables

8.4 Polynomial Inequalities and Rational Inequalities

**9. More On Systems**

9.1 Systems of Equations in Three Variables

9.2 Solving Applications: Systems of Three Equations

9.3 Elimination Using Matrices

Mid-Chapter Review

9.4 Determinants and Cramer’s Rule

9.5 Business and Economic Applications

**10. Exponents and Radical Functions**

10.1 Radical Expressions, Functions, and Models

10.2 Rational Numbers as Exponents

10.3 Multiplying Radical Expressions

10.4 Dividing Radical Expressions

10.5 Expressions Containing Several Radical Terms

Mid-Chapter Review

10.6 Solving Radical Equations

10.7 The Distance Formula, the Midpoint Formula, and Other Applications

10.8 The Complex Numbers

**11. Quadratic Functions and Equations**

11.1 Quadratic Equations

11.2 The Quadratic Formula

11.3 Studying Solutions of Quadratic Equations

11.4 Applications Involving Quadratic Equations

11.5 Equations Reducible to Quadratic

Mid-Chapter Review

11.6 Quadratic Functions and Their Graphs

11.7 More About Graphing Quadratic Functions

11.8 Problem Solving and Quadratic Equations

**12. Exponential Functions and Logarithmic Functions**

12.1 Composite Functions and Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithmic Functions

Mid-Chapter Review

12.5 Natural Logarithms and Changing Bases

12.6 Solving Exponential and Logarithmic Equations

12.7 Applications of Exponential and Logarithmic Functions

**Marvin Bittinger** has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University–Purdue University Indianapolis, and is now Professor Emeritus of Mathematics Education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana, with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

**David Ellenbogen** has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts—Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing, and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.

**Barbara Johnson** has a BS in mathematics from Bob Jones University and a MS in math from Clemson University. She has taught high school and college math for 25 years, and enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she recently earned a black belt in karate. She currently teaches at Ivy Tech Community College of Indiana.

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