College Algebra with Modeling and Visualization, 6th edition

Published by Pearson (January 1, 2017) © 2018
Gary K. Rockswold

Title overview

For courses in College Algebra.

Develop concepts in context

College Algebra with Modeling and Visualization shows students why math matters. It presents the concept of a function as a unifying theme, with an emphasis on the rule of 4 (verbal, graphical, numerical, and symbolic representations). Students learn the concepts in the context of the world they know, leading to better understanding and retention. From there, the author shows a connection between application, modeling, and visualization.

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.

Hallmark features of this title

  • Applications keep the text relevant with contemporary examples drawn from a variety of real data, enableing students to see the relevance of math and developing their problem-solving skills.
  • Making Connections features show how concepts throughout the course are interrelated by pointing out connections between previously learned material and new material.
  • Cumulative Reviews after every few chapters require students to understand and use multiple skills from different chapters.
  • Robust, built-in study aids:
    • Now Try exercise suggestions after every example allow students to immediately reinforce the concepts as they go. Comment Boxes allow graphs, tables, and symbolic explanations to be labeled in a way that makes concepts easier to understand.
    • Chapter Summary Grids allow students to review quickly with an easy-to-read grid format, listing the Concept and providing an Explanation and Example. Comprehensive end-of-chapter material includes a summary of key concepts, Review Exercises, and Extended and Discovery Exercises.

New to this edition

  • Hundreds of application examples and exercises have been updated for currency and relevance.
  • Over 600 new exercises have been added throughout, at both 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.
  • New 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. New Interpret & Analyze in Context exercises indicate where students need to interpret or analyze math used to describe real life. New Checking Symbolic Skills exercises preview important topics that students will see again in calculus.
  • 8 new Collaborative Activities developed by the author (Appendix A) follow a project-based learning approach. Some activities focus on a specific concept while others span multiple concepts.
  • 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.

Key features

Features of MyLab Math for the 6th Edition

  • See the Concept videos bring key concepts in the text to life show students the math worked out. Each video now has an accompanying MyLab Math assessment question. 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.
  • 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.
    • 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.
  • 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.

Table of contents

1. Introduction to Functions and Graphs

  • 1.1 Numbers, Data, and Problem Solving
  • 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
  • Summary
  • Review Exercises
  • 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
  • Summary
  • Review Exercises
  • 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 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
  • Summary
  • Review Exercises
  • 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
  • Summary
  • Review Exercises
  • 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
  • Summary
  • Review Exercises
  • Extended and Discovery Exercises

6. Systems of Equations and Inequalities

  • 6.1 Functions and Systems of Equations in Two Variables
  • 6.2 Systems of Inequalities in Two Variables
  • Checking Basic Concepts for Sections 6.1 and 6.2
  • 6.3 Systems of Linear Equations in Three Variables
  • 6.4 Solutions to Linear Systems Using Matrices
  • Checking Basic Concepts for Sections 6.3 and 6.4
  • 6.5 Properties and Applications of Matrices
  • 6.6 Inverses of Matrices
  • Checking Basic Concepts for Sections 6.5 and 6.6
  • 6.7 Determinants
  • Checking Basic Concepts for Section 6.7
  • Summary
  • Review Exercises
  • Extended and Discovery Exercises
  • Chapters 1-6 Cumulative Review Exercises

7. Conic Sections

  • 7.1 Parabolas
  • 7.2 Ellipses
  • Checking Basic Concepts for Sections 7.1 and 7.2
  • 7.3 Hyperbolas
  • Checking Basic Concepts for Section 7.3
  • Summary
  • Review Exercises
  • Extended and Discovery Exercises

8. Further Topics in Algebra

  • 8.1 Sequences
  • 8.2 Series
  • Checking Basic Concepts for Sections 8.1 and 8.2
  • 8.3 Counting
  • 8.4 The Binomial Theorem
  • Checking Basic Concepts for Sections 8.3 and 8.4
  • 8.5 Mathematical Induction
  • 8.6 Probability
  • Checking Basic Concepts for Sections 8.5 and 8.6
  • Summary
  • Review Exercises
  • Extended and Discovery Exercises
  • Chapters 1-8 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

Appendices

  • A: Collaborative Activities
  • B: A Library of Functions
  • C: Partial Fractions
  • D: Percent Change and Exponential Functions
 

Author bios

About our author

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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