Student Solutions Manual for College Algebra

Description

New and updated features

• NEW! Just-In-Time Review of prerequisite algebra topics is located at the beginning of the text and  referenced when students need it most. A more comprehensive review is presented in Chapter R, available in MyMathLab.
• 28 Just-In-Time review topics are referenced throughout the text and MyMathLab course to create an efficient review of intermediate algebra topics.
• Just-In-Time icons appear next to examples where review of an intermediate algebra topic would be helpful, directing students to the review topics in the front of the text.
• These are assignable in MyMathLab so students who need the extra help can get it.

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! Ongoing Review is placed as needed throughout the text and MyMathLab course.
• NEW! Just-In-Time Review of prerequisite algebra topics is now referenced when students need it most.
• 28 Just-In-Time review topics are referenced throughout the text and MyMathLab course to create an efficient review of intermediate algebra topics.
• Just-In-Time icons appear next to examples where review of an intermediate algebra topic would be helpful, directing students to the review topics in the front of the text.
• These are assignable in MyMathLab so students who need the extra help can get it.
• Even more timely review resources are available in the MyMathLab course with the Getting Ready MyMathLab assignments.
• NEW! Chapter R has been moved to MyMathLab. Students and instructors can still utilize this entire review chapter within MyMathLab when they want to supplement the prerequisite topics of the Just-in-Time review with more in-depth coverage and exercises.
• A variety of assignable exercise types are included in the MyMathLab course.
• NEW! Cumulative Review Assignments help promote enhanced concept review. You can assign these pre-made assignments to help students synthesize and retain concepts learned throughout the course.
• NEW! Skill Maintenance Quizzes are pre-made quizzes generated from the Skill Maintenance Exercises found in the text; they support ongoing review to help students maintain essential skills.
• Exercises are now data informed:the authors have revised the exercises, informed by analysis of MyMathLab usage data, for this new edition. The ultimate goal is to improve the quality and quantity of the exercises that matter most to both instructors and students. For example, the authors adjusted the sample homework assignments to ensure usage of the most widely-used exercises.
• Example-based Videos in MyMathLab are created by the authors and walk students through the detailed solution process for key examples in the textbook. Videos have optional subtitles.
• NEW! Video Assessment Exercises correlate with the Example-based Videos to help check for conceptual understanding.This combination is a great way to ensure that students watched and understood the video material.
• NEW! The Video Notebook contains fill-in-the-blank worksheets to accompany the video examples presented by the authors. After watching the video and filling in the worksheet, students have an excellent study guide for review and test preparation.
• NEW! Skills for Success Modules are integrated into the MyMathLab course to help students develop the good habits needed in the transition to college and then to professional life.
• NEW! Guided Visualizations are engaging interactive figures that bring mathematical concepts to life, helping students see the concepts through directed explorations and purposeful manipulation. These figures are assignable in MyMathLab and encourage active learning, critical thinking, and conceptual understanding.

1. Graphs, Functions, and Models
   • 1.1. Introduction to Graphing
     • Visualizing the Graph
   • 1.2. Functions and Graphs
   • 1.3. Linear Functions, Slope, and Applications
     • Visualizing the Graph
     • Mid-Chapter Mixed Review
   • 1.4. Equations of Lines and Modeling
   • 1.5. Linear Equations, Functions, Zeros, and Applications
   • 1.6. Solving Linear Inequalities
   • Summary and Review
   • Review Exercises
   • Chapter Test
2. More on Functions
   • 2.1. Increasing, Decreasing, and Piecewise Functions; Applications
   • 2.2. The Algebra of Functions
   • 2.3. The Composition of Functions
     • Mid-Chapter Mixed Review
   • 2.4. Symmetry
   • 2.5. Transformations
     • Visualizing the Graph
   • 2.6. Variation and Applications
   • Summary and Review
   • Review Exercises
   • Chapter Test
3. Quadratic Functions and Equations; Inequalities
   • 3.1. The Complex Numbers
   • 3.2. Quadratic Equations, Functions, Zeros, and Models
   • 3.3. Analyzing Graphs of Quadratic Functions
     • Visualizing the Graph
     • Mid-Chapter Mixed Review
   • 3.4. Solving Rational Equations and Radical Equations
   • 3.5. Solving Equations and Inequalities with Absolute Value
     • Summary and Review
     • Review Exercises
     • Chapter Test
4. Polynomial Functions and Rational Functions
   • 4.1. Polynomial Functions and Modeling
   • 4.2. Graphing Polynomial Functions
     • Visualizing the Graph
   • 4.3. Polynomial Division; The Remainder Theorem and the Factor Theorem
     • Mid-Chapter Mixed Review
   • 4.4. Theorems about Zeros of Polynomial Functions
   • 4.5. Rational Functions
     • Visualizing the Graph
   • 4.6. Polynomial Inequalities and Rational Inequalities
     • Study Guide
     • Review Exercises
     • Chapter Test
5. Exponential Functions and Logarithmic Functions
   • 5.1. Inverse Functions
   • 5.2. Exponential Functions and Graphs
   • 5.3. Logarithmic Functions and Graphs
     • Visualizing the Graph
     • Mid-Chapter Mixed Review
   • 5.4. Properties of Logarithmic Functions
   • 5.5. Solving Exponential Equations and Logarithmic Equations
   • 5.6. Applications and Models: Growth and Decay; Compound Interest 364
     • Study Guide
     • Review Exercises
     • Chapter Test
6. Systems of Equations and Matrices
   • 6.1. Systems of Equations in Two Variables
     • Visualizing the Graph
   • 6.2. Systems of Equations in Three Variables
   • 6.3. Matrices and Systems of Equations
   • 6.4. Matrix Operations
     • Mid-Chapter Mixed Review
   • 6.5. Inverses of Matrices
   • 6.6. Determinants and Cramer’s Rule
   • 6.7. Systems of Inequalities and Linear Programming
   • 6.8. Partial Fractions
     • Study Guide
     • Review Exercises
     • Chapter Test
7. Conic Sections
   • 7.1. The Parabola
   • 7.2. The Circle and the Ellipse
     • Mid-Chapter Mixed Review
   • 7.3. The Hyperbola
   • 7.4. Nonlinear Systems of Equations and Inequalities
     • Visualizing the Graph
     • Study Guide
     • Review Exercises
     • Chapter Test
8. Sequences, Series, and Combinatorics
   • 8.1. Sequences and Series
   • 8.2. Arithmetic Sequences and Series
   • 8.3. Geometric Sequences and Series
     • Visualizing the Graph
   • 8.4. Mathematical Induction
     • Mid-Chapter Mixed Review
   • 8.5. Combinatorics: Permutations
   • 8.6. Combinatorics: Combinations
   • 8.7. The Binomial Theorem
   • 8.8. Probability
     • Study Guide
     • Review Exercises
     • Chapter Test

Photo Credits

Answers

Additional Instructor’s Answers

Index

Index of Applications

This manual contains completely worked-out solutions for all the odd-numbered exercises in the text.

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. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled “Baseball and Mathematics.” 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.

Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University—Purdue University Indianapolis. In addition to her career in textbook publishing, she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children’s camp.

David Ellenbogen has taught math at the college level for twenty-two 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 also 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 since 1985, having served on its Developmental Mathematics Committee and as a delegate, and has been a member of the Mathematical Association of America since 1979. He has authored dozens of publications on topics ranging from prealgebra to calculus and has delivered lectures at numerous conferences on the use of language in mathematics. Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from The University of Massachusetts at Amherst. A co-founder of the Colchester Vermont Recycling Program, Professor Ellenbogen has a deep love for the environment and the outdoors, especially in his home state of Vermont. In his spare time, he enjoys playing keyboard in the band Soularium, volunteering as a community mentor, hiking, biking, and skiing. He has two sons, Monroe and Zack.

Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University—Purdue University Indianapolis and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit, and spend time with her children.

About the Book

• Functions appear early and are integrated throughout the text, reflecting the authors’ belief that functions are best taught as a theme of the course—not as an isolated topic.
• Functions are introduced in Chapter 1, so that students start the course with a new topic rather than a review of equation-solving that was covered in previous math courses.
• Students come to understand the concept of a function by being exposed repeatedly to the language, notation, and use of functions throughout the text.
• Graphs are used frequently to provide a visual component to solving equations and inequalities.
• The visual approach of the authors enables students to “see the math” and quickly make connections between concepts.
• Visualizing the Graph exercises help develop students’ ability to make the mental link between different types of equations and their corresponding graphs. In addition to the full-page feature within the chapters, a unique exercise-type asks students to match equations with their graphs.
• Algebraic/Graphical Side-by-Side Examples present the solutions in a two-column format to help students understand the connection between algebraic manipulation and the graphical interpretation.
• Guided Visualizations are available in MyMathLab, enabling users to manipulate figures to bring hard-to-convey math concepts to life. These are also assignable, giving instructors one more tool to promote understanding.
• Annotated Examples show step-by-step procedures, and employ color-coded art to guide students through the process of learning and understanding the concepts.
• Now Try questions, following every example, encourage active learning by asking students to do an exercise in the exercise set that is similar to the example.
• Ongoing review features throughout the text reinforce the concepts and help students build understanding.
• NEW! Just-In-Time Review of prerequisite algebra topics is located at the beginning of the text and  referenced when students need it most. A more comprehensive review is presented in Chapter R, available in MyMathLab.
• 28 Just-In-Time review topics are referenced throughout the text and MyMathLab course to create an efficient review of intermediate algebra topics.
• Just-In-Time icons appear next to examples where review of an intermediate algebra topic would be helpful, directing students to the review topics in the front of the text.
• These are assignable in MyMathLab so students who need the extra help can get it.
• Mid-Chapter Mixed Review Exercises offer ongoing review, with one-page mixed review sets at logical breaks in the chapter. These help students reinforce their understanding of the concepts and are assignable in MyMathLab.
• Study Guides have been added to the Summary and Review, giving students a built-in study aid when reviewing and preparing for tests. In MyMathLab, these Study Guides are accompanied by narrated examples to reinforce the key concepts and ideas.
• A Chapter Test at the end of each chapter allows students to test themselves and target all areas that need further study before taking the in-class exam.
• Section Objectives are listed at the beginning of each section. Together with subheadings throughout the section, these objectives provide a useful outline of the section for both instructors and students.
• Making connections is an important part of successfully learning and retaining math concepts, so the authors draw connections throughout the text.
• Connecting the Concepts, a hallmark feature of the text, invites the student to stop and check their understanding of how c

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