# Algebra and Trigonometry with Modeling & Visualization, 6th edition

Published by Pearson (January 19, 2017) © 2018

**Gary K. Rockswold**Minnesota State University, Mankato

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## MyLab

- Reach every student with personalized support
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*For courses in **Algebra and Trigonometry.*

**Showing why math matters **

Gary Rockswold doesn’t just mention real-world examples; he teaches mathematical concepts *through *those applications. For example, if we look at Facebook usage over time, what might that tell us about linear growth and predictions? In this way, students learn the concepts in the context of the world they know, which leads to better understanding and retention. From there, the author shows a connection between application, modeling, and visualization. Rockswold is known for presenting the concept of a function as a unifying theme, with an emphasis on the rule of four (verbal, graphical, numerical, and symbolic representations). The 6th Edition emphasizes conceptual understanding with new in-chapter features and assignment options, while at the same time providing tools to empower instructors to make their classroom more active through collaboration and group work.

**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 6th Edition continues to expand the comprehensive auto-graded exercise options. The pre-existing exercises were carefully reviewed, vetted, and improved using aggregated student usage and performance data over time. In addition, MyLab Math includes new options to support conceptual learning, visualization, and student preparedness.

Students, if interested in purchasing this title with MyLab Math, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

**Draw students in with a real example to set up and teach the core precalculus topics****Applications**keep the text relevant for students with contemporary examples that draw from a variety of real data and enable students to see the relevance of math, helping them to become more effective problem-solvers.**UPDATED! Hundreds of application examples and exercises**have been updated to bring timely meaning and relevance to the mathematics.

**Move students beyond isolated skills by emphasizing conceptual understanding.****NEW! See the Concept**boxes are a hallmark feature, allowing students to make important connections by walking them through detailed visualisations. Students use graphs, tables, and diagrams to learn new concepts in a concise and efficient way.**Making Connections**features show how concepts throughout the course are interrelated by pointing out connections between previously learned material and new material.**NEW!**For examples that require multi-step solutions, the author builds in**Getting Started pointers**, which help students develop an overall problem-solving strategy before they begin writing a detailed solution.

**Provide a more active or flipped classroom**with**new opportunities for collaborative learning and in-class group work.****NEW! 8 New Collaborative Activities,**developed by the author as Appendix A, follow a project-based learning approach. Students actively explore real-world challenges and apply what they know to produce results that matter. Some activities focus on a specific concept while others span multiple concepts, requiring students to synthesise their knowledge.**NEW!**The**Guided Notebook with Integrated Review Worksheets**is ideal for flipped classrooms or any class looking to incorporate more group work and activities. Authored by Laura J. Younts (Santa Fe College) as a one-stop-shop for student engagement, each section contains a structured lecture outline that students fill in during lecture, followed by a group activity to complete in class. It also includes reflection sections to let students record questions they have, space for the work to be done at home, and extended projects for most chapters. Also included are Integrated Review worksheets, which offer additional practice exercise of intermediate algebra topics with ample space for students to show their work.

**Tailor assignments to instructor course approach and problem-solving support to student learning with a wide variety of assignment options.****New! Over 600 new exercises were added to the 6th Edition,**giving students even more abundant opportunities for practice and review. Each set of exercises covers skill building, mathematical concepts, and applications. Graphical interpretation and tables of data are often used to extend students’ understanding of mathematical concepts. Additional exercise sets include Word problems, Checking Basic Concepts, Chapter Review Exercises, Extended and Discovery Exercises, and Writing About Mathematics.**NEW! Additional exercise types**lend more flexibility for instructors, including**Critical Thinking**exercises and**Interpret & Analyze in Context exercises**that ask students to interpret math used in real life.**Checking Symbolic Skills**exercises provide a preview into important topics that students will see again in calculus.**Cumulative Reviews**, which appear every few chapters, require students to understand and use multiple skills from different chapters. This is an e

**Personalize learning 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. For the 6th Edition, “See the Concept,” “Getting Ready,” and “Putting It All Together” questions are now rendered and can be assigned in MyLab Math. Video assessment questions help students have a more meaningful experience with the concepts presented, and interactive figures allow students to visualize difficult topics.

**See the Concept videos**bring key concepts in the text to life and allow students to benefit from seeing the math worked out. Videos are also integrated throughout the eText for immediate access when students need it most and are available in the Multimedia Library for easy in-class use. Each**See the Concept**video now has an accompanying MyLab Math assessment question, making these videos truly assignable .**NEW! Set Up & Solve exercises**require students to show the setup of the solution for a particular exercise as well as the solution, helping them develop an overall problem-solving strategy before attempting the solution. These align with the in-chapter examples that include Getting Started steps.**Putting It All Together**at the end of every section summarizes techniques and reinforces the mathematical concepts presented in the section in an easy-to-follow grid. For the 6th Edition,**Putting It All Together**questions are assignable in MyLab Math as conceptual questions, asking students to classify, sort, categorize, or order mathematical expressions, graphs, and terms.**Foster student engagement and peer-to-peer learning****NEW! Learning Catalytics**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.^{™ }- Upload a full PowerPoint
^{®}deck for easy creation of slide questions. - Team names are no longer case sensitive.
- Help your students develop critical thinking skills.
- Monitor responses to find out where your students are struggling.
- Rely on real-time data to adjust your teaching strategy.
- Automatically group students for discussion, teamwork, and peer-to-peer learning.

**About the Book**

**See the Concept**boxes are a hallmark feature, allowing students to make important connections by walking them through detailed visualizations. Students use graphs, tables, and diagrams to learn new concepts in a concise and efficient way. New to the 6th Edition, See the Concept Videos in MyLab Math bring key concepts to life and are assignable via assessment questions.**New Exercise Types emphasize conceptual understanding and connections to calculus.****Critical Thinking**exercises ask students to take a mathematical concept a step further than what is discussed in the text. They challenge students to think beyond the pages of the book.**Interpret & Analyze in Context**exercises indicate where students need to interpret or analyze math used to describe real life.**Checking Symbolic Skills**exercises provide a preview into important topics that students will see again in calculus.**8 New Collaborative Activities,**developed by the author as Appendix A, follow a project-based learning approach. Students actively explore real-world challenges and apply what they know to produce results that matter. Some activities focus on a specific concept while others span multiple concepts, requiring students to synthesize their knowledge.- The
**Guided Notebook with Integrated Review Worksheets**, available in MyLab Math or as a print supplement, is ideal for flipped classrooms or any class looking to incorporate more group work and activities. - Authored by Laura J. Younts (Santa Fe College) as a one-stop-shop for student engagement, each section contains a structured lecture outline that students fill in during lecture, followed by a group activity to complete in class. It also includes reflection sections to let students record questions they have, space for the work to be done at home, and extended projects for most chapters.
- The
**Integrated Review Worksheets**offer additional practice exercises of relevant intermediate algebra topics with ample space for students to show their work. These are included in the Guided Notebook as well as within the MyLab Math Integrated Review course option, which is designed to bring underprepared students up to speed. **Data-Driven Revision:**The author analyzed the aggregated student usage and performance data in MyLab Math over time. This data was used to adjust exercise difficulty levels, to add coverage in the text and in MyLab Math, and ensure a smooth progression from simpler to more challenging exercises.**Hundreds of application examples and exercises**have been updated to bring timely meaning and relevance to the mathematics.**Over 600 new exercises**have been added throughout the text, both at the basic and higher levels of difficulty.**More critical thinking about graphical interpretation**has been added. These examples and exercises often ask students to identify characteristics of a graph, such as intercepts, zeros, extrema, and intervals where the graph is increasing or decreasing.

**Content Updates**

**The definition of intercept**has been changed to be a point, rather than a real number, at the request of reviewers.**More emphasis on domain and range**in context has been included.**Chapter 1**includes the new topics of finding percent change and the center of a circle by completing the square. Interval notation is now introduced in Chapter 1. More discussion of graphing linear functions by hand, interpreting domain and range in context, applying the Pythagorean theorem, and determining an appropriate calculator window have been added.**Chapter 2**has additional examples and exercises covering piecewise-defined functions, absolute value inequalities, and critical thinking about graphs of functions. A new subsection on percentages has been included and a more complete discussion of the*x*–intercept method has also been added.**Chapter 3**now has a graphical derivation of the vertex formula that is student accessible. There is additional emphasis on domain and range in context and also identifying the domain and range of translated and reflected functions.**Chapter 4**has a new subsection covering graphs of power functions having integer exponents. Much of Section 4.2 has been rewritten to make it more accessible for students.**Chapter 5**has a new subsection covering exponential and logarithmic inequalities. More discussion of linear and exponential growth, simplifying functions and their domains, and logarithmic and exponential forms has been added. More modeling examples and exercises that require students to select a modeling function have been added to Section 5.7.**Chapter 6**has new coverage of supply and demand applications along with finding equilibrium prices and quantities. Additional business and social network applications have also been added. A new discussion of steps for solving a system of equations using the elimination method has been included.**Chapter 7**has new examples and exercises for finding the standard equation of a circle by completing the square.**Chapter 8**has new*See the Concept*boxes that help explain the distinction between arithmetic and geometric sequences.**Appendix A**is new and contains several Collaborative Activities that can be completed in or out of class. These activities, or projects, are application-based and include discussion of results and often require connections with previous concepts.

1. Introduction to Functions and Graphs

1.1 Numbers, Data, and Problem Solving

1.2 Visualizing and Graphing Data

Checking Basic Concepts for Sections 1.1 and 1.2

1.3 Functions and Their Representations

1.4 Types of Functions and Their Rates of Change

Checking Basic Concepts for Sections 1.3 and 1.4

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Extended and Discovery Exercises

2. Linear Functions and Equations

2.1 Equations of Lines

2.2 Linear Equations

Checking Basic Concepts for Sections 2.1 and 2.2

2.3 Linear Inequalities

2.4 More Modeling with Functions

Checking Basic Concepts for Sections 2.3 and 2.4

2.5 Absolute Value Equations and Inequalities

Checking Basic Concepts for Section 2.5

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Extended and Discovery Exercises

Chapters 1-2 Cumulative Review Exercises

3. Quadratic Functions and Equations

3.1 Quadratic Functions and Models

3.2 Quadratic Equations and Problem Solving

Checking Basic Concepts for Sections 3.1 and 3.2

3.3 Complex Numbers

3.4 Quadratic Inequalities

Checking Basic Concepts for Sections 3.3 and 3.4

3.5 Transformations of Graphs

Checking Basic Concepts for Section 3.5

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Extended and Discovery Exercises

4. More Nonlinear Functions and Equations

4.1 More Nonlinear Functions and Their Graphs

4.2 Polynomial Functions and Models

Checking Basic Concepts for Sections 4.1 and 4.2

4.3 Division of Polynomials

4.4 Real Zeros of Polynomial Functions

Checking Basic Concepts for Sections 4.3 and 4.4

4.5 The Fundamental Theorem of Algebra

4.6 Rational Functions and Models

Checking Basic Concepts for Sections 4.5 and 4.6

4.7 More Equations and Inequalities

4.8 Radical Equations and Power Functions

Checking Basic Concepts for Sections 4.7 and 4.8

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Extended and Discovery Exercises

Chapters 1-4 Cumulative Review Exercises

5. Exponential and Logarithmic Functions

5.1 Combining Functions

5.2 Inverse Functions and Their Representations

Checking Basic Concepts for Sections 5.1 and 5.2

5.3 Exponential Functions and Models

5.4 Logarithmic Functions and Models

Checking Basic Concepts for Sections 5.3 and 5.4

5.5 Properties of Logarithms

5.6 Exponential and Logarithmic Equations

Checking Basic Concepts for Sections 5.5 and 5.6

5.7 Constructing Nonlinear Models

Checking Basic Concepts for Section 5.7

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Extended and Discovery Exercises

6. Trigonometric Functions

6.1 Angles and Their Measure

6.2 Right Triangle Trigonometry

Checking Basic Concepts for Sections 6.1 and 6.2

6.3 The Sine and Cosine Functions and Their Graphs

6.4 Other Trigonometric Functions and Their Graphs

Checking Basic Concepts for Sections 6.3 and 6.4

6.5 Graphing Trigonometric Functions

6.6 Inverse Trigonometric Functions

Checking Basic Concepts for Sections 6.5 and 6.6

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Extended and Discovery Exercises

Chapters 1-6 Cumulative Review Exercises

7. Trigonometric Identities and Equations

7.1 Fundamental Identities

7.2 Verifying Identities

Checking Basic Concepts for Sections 7.1 and 7.2

7.3 Trigonometric Equations

7.4 Sum and Difference Identities

Checking Basic Concepts for Sections 7.3 and 7.4

7.5 Multiple-Angle Identities

Checking Basic Concepts for Section 7.5

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Extended and Discovery Exercises

8. Further Topics in Trigonometry

8.1 Law of Sines

8.2 Law of Cosines

Checking Basic Concepts for Sections 8.1 and 8.2

8.3 Vectors

8.4 Parametric Equations

Checking Basic Concepts for Sections 8.3 and 8.4

8.5 Polar Equations

8.6 Trigonometric Form and Roots of Complex Numbers

Checking Basic Concepts for Sections 8.5 and 8.6

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Extended and Discovery Exercises

Chapters 1-8 Cumulative Review Exercises

9. Systems of Equations and Inequalities

9.1 Functions and Systems of Equations in Two Variables

9.2 Systems of Inequalities in Two Variables

Checking Basic Concepts for Sections 9.1 and 9.2

9.3 Systems of Linear Equations in Three Variables

9.4 Solutions to Linear Systems Using Matrices

Checking Basic Concepts for Sections 9.3 and 9.4

9.5 Properties and Applications of Matrices

9.6 Inverses of Matrices

Checking Basic Concepts for Sections 9.5 and 9.6

9.7 Determinants

Checking Basic Concepts for Section 9.7

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Extended and Discovery Exercises

Chapters 1-9 Cumulative Review Exercises

10. Conic Sections

10.1 Parabolas

10.2 Ellipses

Checking Basic Concepts for Sections 10.1 and 10.2

10.3 Hyperbolas

Checking Basic Concepts for Section 10.3

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Extended and Discovery Exercises

11. Further Topics in Algebra

11.1 Sequences

11.2 Series

Checking Basic Concepts for Sections 11.1 and 11.2

11.3 Counting

11.4 The Binomial Theorem

Checking Basic Concepts for Sections 11.3 and 11.4

11.5 Mathematical Induction

11.6 Probability

Checking Basic Concepts for Sections 11.5 and 11.6

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Extended and Discovery Exercises

Chapters 1-11 Cumulative Review Exercises

R. Reference: Basic Concepts from Algebra and Geometry

R.1 Formulas from Geometry

R.2 Integer Exponents

R.3 Polynomial Expressions

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Radical Notation and Rational Exponents

R.7 Radical Expressions

Appendix A: Using the Graphing Calculator

Appendix B: A Library of Functions

Appendix C: Partial Fractions

Appendix D: Percent Change and Exponential Functions

Appendix E: Rotation of Axes

Bibliography

Answers to Selected Exercises

Photo Credits

Index of Applications

Index

**Gary Rockswold **has taught mathematics, computer science, and physical science at a wide variety of levels, including high school, undergraduate, and graduate students for over 30 years. He received his bachelor’s degree from St. Olaf College and his Ph.D. in applied mathematics from Iowa State University. He has been a principal investigator of parallel computing at the Minnesota Supercomputer Institute and is an emeritus professor of mathematics at Minnesota State University, Mankato. He is an author and has published numerous mathematics textbooks for Pearson Education at both the developmental and collegiate levels. His motivation for writing is to make mathematics more inclusive for a greater number of students by presenting mathematics in a contextual, meaningful way.

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