Beginning and Intermediate Algebra with Applications & Visualization, 4th edition

Published by Pearson (January 1, 2017) © 2018

  • Gary K. Rockswold Minnesota State University, Mankato
  • Terry A. Krieger Rochester Community and Technical College

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For courses in Prealgebra & Beginning Algebra.

The Rockswold/Krieger algebra series fosters conceptual understanding by developing concepts in context through the use of applications, multiple representations, and visualization. By seeing the concept in context before being given the the mathematical abstraction, students make math part of their own experiences instead of just memorizing techniques. The authors believe this approach deepens conceptual understanding and better prepares students for future math courses and life. The new edition continues to bring concepts to life with even more opportunities for students to visualize the math in real-world contexts-–and so, learn key critical-thinking and problem-solving skills-–with new features in the text and MyLab Math. 

                                                                                                                              

Also Available with MyLab Math.

MyLab Math 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 4th Edition continues to help students develop conceptual understanding and bring key concepts to life with content and assignments that reflect the authors’ approach, including new Section Introduction videos and See the Concept videos with assessment. New Skill Builder assignments offer adaptive practice to build students’ foundational skills, and new workspace assignments allow students to show their mathematical reasoning as they progress step-by-step, with specific feedback at each step in the problem-solving process that adjusts to their path. 


About this book

                                   

Experiencing Math in Context: Rockswold/Krieger’s unique approach presents students with the math in context first, before explaining the abstract mathematical theory behind it. This gives students a familiar and concrete foundation to build the concepts on. Math in the context of the real world is emphasized throughout–-both to engage students’ interest, and to help them grasp mathematical concepts through tangible applications.

  • NEW! Connecting Concepts with Your Life reinforces students’ knowledge needed to understand a new concept. The new Connecting Concepts with Your Life feature gives meaning to mathematics by relating common life experiences that students already understand
  • NEW! Math in Context engages students by connecting mathematics to current and relevant topics. This new feature helps students recognize when and how math connects to everyday life
  • UPDATED! Applications engage students by connecting mathematics to current and relevant topics. Several new examples have been added that discuss the mathematics of the Internet, social networking, tablet computers, and other contemporary topics
  • NEW! Modeling Data in hundreds of exercises and examples offer students the chance to model real and relevant data with their own functions
  • NEW! Online Exploration exercises invite students to find their own data on the Internet and use mathematics to analyze it.  
  • Chapter Openers start each chapter with a contemporary application that motivates students by offering insights into the relevance of that chapter’s mathematical concepts.

Understanding and Visualizing the Concepts: The Rockswold/Krieger approach excels at promoting conceptual understanding above procedural skills. Additionally, an emphasis on visualization provides opportunities for students with different learning styles to successfully absorb the information presented.

  • NEW! See the Concept presents a concise, visual overview of topics that were previously written out as text. Visualizing the math makes it accessible to all students. Companion See the Concept videos in MyLab Math, presented by the authors, help bring the concept to life. Each See the Concept video also has accompanying MyLab Math assessment questions, making these videos truly assignable 
  • Putting It All Together boxes at the end of each section summarize techniques and reinforce the mathematical concepts presented in the section and are also available to be assigned in MyLab Math
  • NEW! Comment Balloons appear next to steps and procedures to make them more (immediately) understandable
  • Learning the Math from Multiple Perspectives presents concepts by means of verbal, graphical, numerical, and symbolic representations to support multiple learning styles and problem-solving methods.
  • New Vocabulary is listed at the start of every section, highlighting the math concepts that are introduced in that section. This gives students a glimpse of the big picture of the section and helps with test preparation
  • Reading Check questions appear alongside important concepts, ensuring that students understand the material they have just read. These are located throughout every section. Many Reading Checks are assignable in MyLab Math
  • Making Connections occur throughout the text and help students see how previous concepts are related to new concepts. Many Making Connections exercises are assignable in MyLab Math
  • Critical Thinking exercises are included in most sections, posing questions that can be used for class discussion, group work, or homework assignments. Selected Critical Thinking features are also available to be assigned in MyLab Math
  • NEW! Guided Workbook is keyed to the text by section and objective and leads students through the course, giving them the opportunity to record key information, work practice problems, and show and keep their work for reference—as well as taking conceptual understanding one step further by asking students to explain Why? after select questions.                                                                                                                                                                                                     

Practicing and Mastering the Concepts: Ample opportunity for students to practice and review the concepts and skills ensures students retain what they’ve learned.                

  • Now Try exercises follow every example for immediate reinforcement of the skills and concepts
  • NEW! Objective Lists at the beginning of each section give a clear outline of the section contents, making it easier to customize the course
  • Concepts and Vocabulary exercises appear in every section
  • Checking Basic Concepts exercises appear after every other section and can be used for individual or group review. These exercises require 10–20 minutes to complete and are also appropriate for in-class work.
  • Thinking Generally encourage students to synthesize what they have just learned with open-ended conceptual questions that appear in most section exercise sets.
  • Writing about Mathematics exercises appear at the end of most sections. Students are asked to explain the concepts behind the mathematical procedures they just learned in their own words, encouraging true understanding instead of simple rote memorization.
  • Group Activities appear once or twice per chapter and provide an opportunity for students to work collaboratively on a problem that involves real-world data. Most activities can be completed with limited use of class time. 
  • Using a Graphing Calculator
    • Graphing Calculator Exercise icons denote an optional exercise that requires students to have access to a graphing calculator.
    • Technology Notes throughout the text are optional notes that offer students guidance, suggestions, and caution.
  • Study Tips offer just-in-time suggestions to help students stay organized and focused on the material at hand
  • Chapter Summary combines key terms, topics, and procedures with illuminating examples to assist students as they prepare for the test with a quick but thorough review
  • Chapter Review Exercises requires students to work exercises and gain confidence while mastering the material
  • Chapter Tests provide students with rehearsal for the real thing and help reduce math anxiety. Chapter Test Prep Videos offer additional help by showing an instructor working through the step-by-step solutions to every exercise in each Chapter Test
  • Cumulative Review Exercises Starting with Chapter 2 and appearing in all subsequent chapters, Cumulative Review Exercises help students see the big picture of math by reviewing topics and skills they have already learned.                                     


Also Available with MyLab Math.

MyLab Math 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 4th Edition continues to help students develop conceptual understanding and bring key concepts to life with content and assignments that reflect the authors’ approach, including new Section Introduction videos and See the Concept videos with assessment. New Skill Builder assignments offer adaptive practice to build students’ foundational skills, and new workspace assignments allow students to show their mathematical reasoning as they progress step-by-step, with specific feedback at each step in the problem-solving process that adjusts to their path. 


NEW! Expanded assignable content brings the hallmark Rockswold/Krieger approach into the MyLab course

  • NEW! See the Concept videos, created entirely by the authors,bring key concepts to life by providing a visual overview of each See the Concept feature in the text. Visualizing the math makes the content accessible to all students
  • NEW! Section Introduction videos, also created entirely by the authors, are available for every section of the text. These videos introduce the section’s concepts in a contextual setting, giving students an engaging and concrete introduction to the topics they’ll explore
  • NEW! Video assessment questions are available for all See the Concept and Section Introduction videos. This allows instructors to assign the video and encourage students to watch them to reinforce conceptual understanding. In addition to Section Introduction and See the Concept videos, the complete video programincludes section lectures, objective-level videos, and example-level videos, along with Chapter Test Prep videos that cover complete solutions from the Chapter Tests
  • EXPANDED! In addition to end of section exercises, additional content from the text, including many of the Reading Checks, Making Connections, and Critical Thinking features, is available in MyLab Math for instructors to assign
  • NEW! Drag and Drop exercises allow students to manually select elements of the question, such as expressions, words, graphs, or images, and place them into a designated target area. This interactive, new exercise type assesses and reinforces students’ grasp of key concepts
  • NEW! A three-step learning path in MyLab Math encourages students to first Connect with the Math, then Review, and then Practice. The learning path encourages students to take advantage of the resources in their course, such as the See the Concept videos, and to review the section, before going right to their assignments
  • NEW! Guided Workbook is keyed to the text by section and objective and leads students through the course, giving them the opportunity to record key information, work practice problems, and show and keep their work for reference—as well as taking conceptual understanding one step further by asking students to explain Why? after select questions.

NEW! Expanded functionality makes MyLab Math more personalized and targeted than ever

  • NEW! Skill Builder offers adaptive practice to build students’ foundational skills as they complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives
  • NEW! Workspace Assignments allow students to show their mathematical reasoning as they progress step-by-step, with specific feedback at each step in the problem-solving process that adjusts to their path. When accessed via a mobile device, workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus
  • NEW! An Integrated Review MyLab Math course is an alternate version of the MyLab Math course that provides the full suite of supporting resources for Beginning & Intermediate Algebra, plus additional assignments and study aids for students who will benefit from remediation on prerequisite topics. Assignments for the integrated review content are preassigned in MyLab Math, making it easier than ever to create your course!

NEW! Foster student engagement and peer-to-peer learning

  • NEW! Learning Catalytics is available through MyLab Math, and helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking. A library of premade developmental math questions are available in MyLab Math to give instructors a starting point for using this classroom engagement tool.

                                                            

About this book

                                

Experiencing Math in Context: Rockswold/Krieger’s unique approach presents students with the math in context first, before explaining the abstract mathematical theory behind it. This gives students a familiar and concrete foundation to build the concepts on. Math in the context of the real world is emphasized throughout - both to engage students’ interest, and to help them grasp mathematical concepts through tangible applications.

  • Connecting Concepts with Your Life reinforces students’ knowledge needed to understand a new concept. The new Connecting Concepts with Your Life feature gives meaning to mathematics by relating common life experiences that students already understand
  • Math in Context engages students by connecting mathematics to current and relevant topics. This new feature helps students recognize when and how math connects to everyday life
  • UPDATED! Applications engage students by connecting mathematics to current and relevant topics. Several new examples have been added that discuss the mathematics of the Internet, social networking, tablet computers, and other contemporary topics
  • Modeling Data in hundreds of exercises and examples offer students the chance to model real and relevant data with their own functions
  • Online Exploration exercises invite students to find their own data on the Internet and use mathematics to analyze it.  

Understanding and Visualizing the Concepts: The Rockswold/Krieger approach excels at promoting conceptual understanding above procedural skills. Additionally, an emphasis on visualization provides opportunities for students with different learning styles to successfully absorb the information presented.

  • See the Concept presents a concise, visual overview of topics that were previously written out as text. Visualizing the math makes it accessible to all students. Companion See the Concept videos in MyLab Math, presented by the authors, help bring the concept to life. Each See the Concept video also has accompanying MyLab Math assessment questions, making these videos truly assignable
  • Comment Balloons appear next to steps and procedures to make them more (immediately) understandable
  • Guided Workbook is keyed to the text by section and objective and leads students through the course, giving them the opportunity to record key information, work practice problems, and show and keep their work for reference–as well as taking conceptual understanding one step further by asking students to explain Why? after select questions.                                                                                                                                                                                                     

Practicing and Mastering the Concepts: Ample opportunity for students to practice and review the concepts and skills ensures students retain what they’ve learned.                 

  • Objective Lists at the beginning of each section give a clear outline of the section contents, making it easier to customize the course


Also Available with MyLab Math.

MyLab Math 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 4th Edition continues to help students develop conceptual understanding and bring key concepts to life with content and assignments that reflect the authors’ approach, including new Section Introduction videos and See the Concept videos with assessment. New Skill Builder assignments offer adaptive practice to build students’ foundational skills, and new workspace assignments allow students to show their mathematical reasoning as they progress step-by-step, with specific feedback at each step in the problem-solving process that adjusts to their path.  

Expanded assignable content brings the hallmark Rockswold/Krieger approach into the MyLab course

  • See the Concept videos, created entirely by the authors,bring key concepts to life by providing a visual overview of each See the Concept feature in the text. Visualizing the math makes the content accessible to all students
  • Section Introduction videos, also created entirely by the authors, are available for every section of the text. These videos introduce the section’s concepts in a contextual setting, giving students an engaging and concrete introduction to the topics they’ll explore
  • Video assessment questions are available for all See the Concept and Section Introduction videos. This allows instructors to assign the video and encourage students to watch them to reinforce conceptual understanding. In addition to Section Introduction and See the Concept videos, the complete video program includes section lectures, objective-level videos, and example-level videos, along with Chapter Test Prep videos that cover complete solutions from the Chapter Tests
  • EXPANDED! In addition to end of section exercises, additional content from the text, including many of the Reading Checks, Making Connections, and Critical Thinking features, is available in MyLab Math for instructors to assign
  • Drag and Drop exercises allow students to manually select elements of the question, such as expressions, words, graphs, or images, and place them into a designated target area. This interactive, new exercise type assesses and reinforces students’ grasp of key concepts
  • A three-step learning path in MyLab Math encourages students to first Connect with the Math, then Review, and then Practice. The learning path encourages students to take advantage of the resources in their course, such as the See the Concept videos, and to review the section, before going right to their assignments
  • Guided Workbook is keyed to the text by section and objective and leads students through the course, giving them the opportunity to record key information, work practice problems, and show and keep their work for reference–as well as taking conceptual understanding one step further by asking students to explain Why? after select questions.

Expanded functionality makes MyLab Math more personalized and targeted than ever

  • Skill Builder offers adaptive practice to build students’ foundational skills as they complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives
  • Workspace Assignments allow students to show their mathematical reasoning as they progress step-by-step, with specific feedback at each step in the problem-solving process that adjusts to their path. When accessed via a mobile device, workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus
  • An Integrated Review MyLab Math course is an alternate version of the MyLab Math course that provides the full suite of supporting resources for Beginning & Intermediate Algebra, plus additional assignments and study aids for students who will benefit from remediation on prerequisite topics. Assignments for the integrated review content are preassigned in MyLab Math, making it easier than ever to create your course!

Foster student engagement and peer-to-peer learning

  • Learning Catalytics is available through MyLab Math, and helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking. A library of premade developmental math questions are available in MyLab Math to give instructors a starting point for using this classroom engagement tool.

Beginning & Intermediate Algebra Content Changes: In addition to new and updated features, the following refinement of content has taken place for the 4th edition.                                                                   

  • Chapter 1: New exercises were added throughout the chapter, with an emphasis on expanding the coverage of translating words to expressions and identifying parts of a fraction.
  • Chapter 2: A completely new section on unit analysis was added. At the request of reviewers, inequality answers now include interval notation. Over 50 new exercises were also added throughout the chapter, with an emphasis on linear equations and their solutions.
  • Chapter 3: New examples and exercises were added to cover graphing nonlinear equations by hand. Also, at the request of reviewers, intercepts are now identified as ordered pairs rather than a real number.
  • Chapter 4: Supply and demand examples and exercises involving systems of linear equations were added to this chapter.
  • Chapter 5: The exercises pertaining to rules for exponents were expanded and more clearly categorized in the exercise sets.
  • Chapter 6: New examples and exercises that require students to rearrange terms before factoring by grouping were added to this chapter.
  • Chapter 7: The description of least common multiple now includes a more visual, contextual explanation involving the listing method.
  • Chapter 8: We put more emphasis on solving absolute value inequalities symbolically. A new objective that more fully discusses the concept of a relation was inserted before the definition of a function, and exercises were added that give students practice differentiating between relations and functions. Also, a new objective on piecewise-defined functions was added in Section 8.3, with corresponding exercises in both Sections 8.3 and 8.4.
  • Chapter 9: New exercises that ask students to represent simple social networks with matrices were added to this chapter.
  • Chapter 10: The coverage of using zeros to write the formula for a function was expanded in Sections 10.5 and 10.7.
  • Chapter 11: A new graphical description for deriving the formula to find the vertex of a parabola is now included. Also, a real-world example was added to highlight a common situation in which a quadratic equation might have zero, one, or two solutions. This chapter additionally includes increased coverage of complex solutions to quadratic equations.
  • Chapter 12: A discussion connecting social network posts with half-life and exponential decay is now included to give students a relevant and accessible example of this important concept. At the request of reviewers, we expanded the coverage of changing between exponential and logarithmic forms of equations.
  • Chapter 13: New exercises involving the equation of a circle were added.
  • Chapter 14: In this final chapter, the coverage of writing a formula for a sequence from given terms of the sequence was increased.

Table of Contents

  1. Introduction to Algebra
    • 1.1 Numbers, Variables, and Expressions
    • 1.2 Fractions
    • 1.3 Exponents and Order of Operations
    • 1.4 Real Numbers and the Number Line
    • 1.5 Addition and Subtraction of Real Numbers
    • 1.6 Multiplication and Division of Real Numbers
    • 1.7 Properties of Real Numbers
    • 1.8 Simplifying and Writing Algebraic Expressions
  2. Linear Equations and Inequalities
    • 2.1 Introduction to Equations
    • 2.2 Linear Equations
    • 2.3 Introduction to Problem Solving
    • 2.4 Formulas
    • 2.5 Unit Analysis
    • 2.6 Linear Inequalities
  3. Graphing Equations
    • 3.1 Introduction to Graphing
    • 3.2 Equations in Two Variables
    • 3.3 Intercepts; Horizontal and Vertical Lines
    • 3.4 Slope and Rates of Change
    • 3.5 Slope-Intercept Form
    • 3.6 Point-Slope Form
    • 3.7 Introduction to Modeling
  4. Systems of Linear Equations in Two Variables
    • 4.1 Solving Systems of Linear Equations Graphically and Numerically
    • 4.2 Solving Systems of Linear Equations by Substitution
    • 4.3 Solving Systems of Linear Equations by Elimination
    • 4.4 Systems of Linear Inequalities
  5. Polynomials and Exponents
    • 5.1 Rules for Exponents
    • 5.2 Addition and Subtraction of Polynomials
    • 5.3 Multiplication of Polynomials
    • 5.4 Special Products
    • 5.5 Integer Exponents and the Quotient Rule
    • 5.6 Division of Polynomials
  6. Factoring Polynomials and Solving Equations
    • 6.1 Introduction to Factoring
    • 6.2 Factoring Trinomials I (x2 + bx + c)
    • 6.3 Factoring Trinomials II (ax2 + bx + c)
    • 6.4 Special Types of Factoring
    • 6.5 Summary of Factoring
    • 6.6 Solving Equations by Factoring I (Quadratics)
    • 6.7 Solving Equations by Factoring II (Higher Degree)
  7. Rational Expressions
    • 7.1 Introduction to Rational Expressions
    • 7.2 Multiplication and Division of Rational Expressions
    • 7.3 Addition and Subtraction with Like Denominators
    • 7.4 Addition and Subtraction with Unlike Denominators
    • 7.5 Complex Fractions
    • 7.6 Rational Equations and Formulas
    • 7.7 Proportions and Variation
  8. Introduction to Functions
    • 8.1 Functions and Their Representations
    • 8.2 Linear Functions
    • 8.3 Compound Inequalities and Piecewise-Defined Functions
    • 8.4 Other Functions and Their Properties
    • 8.5 Absolute Value Equations and Inequalities
  9. Systems of Linear Equations
    • 9.1 Systems of Linear Equations in Three Variables
    • 9.2 Matrix Solutions of Linear Systems
    • 9.3 Determinants
  10. Radical Expressions and Functions
    • 10.1 Radical Expressions and Functions
    • 10.2 Rational Exponents
    • 10.3 Simplifying Radical Expressions
    • 10.4 Operations on Radical Expressions
    • 10.5 More Radical Functions
    • 10.6 Equations Involving Radical Expressions
    • 10.7 Complex Numbers
  11. Quadratic Functions and Equations
    • 11.1 Quadratic Functions and Their Graphs
    • 11.2 Transformations and Translations of Parabolas
    • 11.3 Quadratic Equations
    • 11.4 The Quadratic Formula
    • 11.5 Quadratic Inequalities
    • 11.6 Equations in Quadratic Form
  12. Exponential and Logarithmic Functions
    • 12.1 Composite and Inverse Functions
    • 12.2 Exponential Functions
    • 12.3 Logarithmic Functions
    • 12.4 Properties of Logarithms
    • 12.5 Exponential and Logarithmic Equations
  13. Conic Sections
    • 13.1 Parabolas and Circles
    • 13.2 Ellipses and Hyperbolas
    • 13.3 Nonlinear Systems of Equations and Inequalities
  14. Sequences and Series
    • 14.1 Sequences
    • 14.2 Arithmetic and Geometric Sequences
    • 14.3 Series
    • 14.4 The Binomial Theorem

Appendix A. Using the Graphing Calculator

Appendix B. Sets

Appendix C. Linear Programming

Appendix D. Synthetic Division

Gary Rockswold has been a professor and teacher of mathematics, computer science, astronomy, and physical science for over 35 years. Not only has he taught at the undergraduate and graduate college levels, but he has also taught middle school, high school, vocational school, and adult education. He received his BA degree with majors in mathematics and physics from St. Olaf College and his PhD in applied mathematics from Iowa State University. He has been a principal investigator at the Minnesota Supercomputer Institute, publishing research articles in numerical analysis and parallel processing. He is currently an emeritus professor of mathematics at Minnesota State University–Mankato. He is an author for Pearson Education and has numerous textbooks at the developmental and precalculus levels. Making mathematics accessible to students and professing the power of mathematics are special passions for Gary. He frequently gives keynote and invited addresses at regional, national, and international math conferences. In his spare time he enjoys sailing, doing yoga, hiking, and spending time with his family.

Terry Krieger has taught mathematics for over 20 years at the middle school, high school, vocational, community college, and university levels. His undergraduate degree in secondary education is from Bemidji State University in Minnesota, where he graduated summa cum laude. He received his MA in mathematics from Minnesota State University–Mankato. In addition to his teaching experience in the United States, Terry has taught mathematics in Tasmania, Australia, and in a rural school in Swaziland, Africa, where he served as a Peace Corps volunteer. Terry has been involved with various aspects of mathematics textbook publication throughout his career. In his free time, Terry enjoys spending time with his wife and two boys, physical fitness, wilderness camping, and trout fishing.

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