# Intermediate Algebra with Applications & Visualization, 5th edition

Published by Pearson (January 30, 2017) © 2018

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

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## MyLab

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For courses in Intermediate 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 5th 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**

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**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

**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) understandableis 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.*Guided Workbook*

**Practicing and Masteri**

**1. Real Numbers and Algebra**

1.1 Describing Data with Sets of Numbers

1.2 Operations on Real Numbers

1.3 Integer Exponents

1.4 Variables, Equations, and Formulas

1.5 Introduction to Graphing

**2. Linear Functions and Models**

2.1 Functions and Their Representations

2.2 Linear Functions

2.3 The Slope of a Line

2.4 Equations of Lines and Linear Models

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**3. Linear Equations and Inequalities**

3.1 Linear Equations

3.2 Introduction to Problem Solving

3.3 Linear Inequalities

3.4 Compound Inequalities and Piecewise-Defined Functions

3.5 Absolute Value Equations and Inequalities

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**4. Systems of Linear Equations**

4.1 Systems of Linear Equations in Two Variables

4.2 The Substitution and Elimination Methods

4.3 Systems of Linear Inequalities

4.4 Introduction to Linear Programming

4.5 Systems of Linear Equations in Three Variables

4.6 Matrix Solutions of Linear Systems

4.7 Determinants

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**5. Polynomial Expressions and Functions**

5.1 Polynomial Functions

5.2 Multiplication of Polynomials

5.3 Factoring Polynomials

5.4 Factoring Trinomials

5.5 Special Types of Factoring

5.6 Summary of Factoring

5.7 Polynomial Equations

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**6. Rational Expressions and Functions**

6.1 Introduction to Rational Functions and Equations

6.2 Multiplication and Division of Rational Expressions

6.3 Addition and Subtraction of Rational Expressions

6.4 Rational Equations

6.5 Complex Fractions

6.6 Modeling with Proportions and Variation

6.7 Division of Polynomials

**7. Radical Expressions and Functions**

7.1 Radical Expressions and Functions

7.2 Rational Exponents

7.3 Simplifying Radical Expressions

7.4 Operations on Radical Expressions

7.5 More Radical Functions

7.6 Equations Involving Radical Expressions

7.7 Complex Numbers

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**8. Quadratic Functions and Equations**

8.1 Quadratic Functions and Their Graphs

8.2 Transformations and Translations of Parabolas

8.3 Quadratic Equations

8.4 The Quadratic Formula

8.5 Quadratic Inequalities

8.6 Equations in Quadratic Form

**9. Exponential and Logarithmic Functions**

9.1 Composite and Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Exponential and Logarithmic Equations

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**10. Conic Sections**

10.1 Parabolas and Circles

10.2 Ellipses and Hyperbolas

10.3 Nonlinear Systems of Equations and Inequalities

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**11. Sequences and Series**

11.1 Sequences

11.2 Arithmetic and Geometric Sequences

11.3 Series

11.4 The Binomial Theorem

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**Appendix A: Using the Graphing Calculator**

**Appendix B: Sets**

**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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