College Algebra in Context with Applications for the Managerial, Life,and Social Sciences

Description

Features

• Applications often draw on real data to prepare students to solve problems in their future courses and careers.
• Chapter openers begin with a brief application that shows how the upcoming material relates to the real world. A small grid lists a few of the applications that students will be seeing in each section, to motivate them to read the text.
• The Algebra Toolbox at the beginning of every chapter provides a “just in time” review of the algebra needed to learn upcoming material. Each Algebra Toolbox begins with a list of Key Concepts, just like the sections in the book, to make this tool even more useful for students.
• Key Concepts are outlined at the beginning of every section. These lists are consistent with the order and organization of the material in the chapter reviews, providing a helpful cross-referencing for exam preparation.
• Skills Check problems precede the exercise sets, allowing students to quickly check if they have read and understood all the concepts needed to complete their homework.
• Exercisesets are designed to test student comprehension by incorporating the algebraic skills covered in the Skills Check with the application problems they will encounter in the real world.
• Chapter review material includes a wealth of material to help students study efficiently.
  • A chapter summary and grid outline Key Concepts and Formulas, which are organized by section and point back to the Key Concepts list at the beginning of each section.
  • Skills Check problems and the exercise sets test students' comprehension of the material in the chapter.
  • Group Activity or Extended Applications are included for instructors to assign as they choose. These problems ask students to apply their knowledge in creative ways, to solidify their grasp of the concepts.

New to this Edition

Content and design changes to this edition make this text an even better teaching and learning tool.

• Annotated Instructor's Edition contains answers for all exercises as well as helpful teaching tips.
• Full-color design improves the detail on graphs and figures and enables highlighting of important concepts and skills.
• Content updates include breaking the content into smaller blocks of topics to allow more flexibility in scheduling quizzes and exams. The first two chapters have each been divided into two chapters. This provides an early milestone for students and makes completing a chapter a less daunting task.
  • Chapter 1 has been divided into two chapters: “Functions, Graphs, and Models; Linear Functions,” and “Linear Models, Equations, and Inequalities.” The order of the sections has remained, so current users will feel comfortable with the flow of the text.
  • Chapter 2 has also been divided into two chapters. “Quadratic and Other Nonlinear Functions” includes quadratic and power functions and models along with piecewise-defined functions. “Additional Topics with Functions” contains the more traditional topics such as transformations and symmetry, combinations and composition of functions, inverse functions, and additional equations and inequalities. With the exception of moving modeling of quadratics and power functions one section sooner, the order of these sections remains unchanged.
• The organization and exposition has been improved throughout the textbook.
  • More discussion and examples provide justification for techniques and opportunities to graph functions with or without technology.
  • The discussion of exact and approximate linear models has been expanded, and the development of linear regression has been improved.
  • The relation among cost, revenue, and profit is now discussed earlier in the text.
  • Quadratic and Power Models has been moved one section earlier in the text, so it is in the same chapter where these functions were introduced.
  • The discussion of piecewise-defined functions has been expanded in Chapter 3, and the section has been renamed to emphasize the importance of piecewise and power functions.
  • In Chapter 5, Exponential and Logarithmic Functions, properties of logarithms are now discussed in Section 5.2, the introductory section on logarithms.
• Two new appendices include a Calculator Guide and an Excel®Guide. Footnotes throughout the text refer students to the appropriate section of the appendices for detailed technology procedures.
• New Narrated Examples Videos with subtitles present key concepts and definitions from the text through narrated examples correlating to the examples in the Graphing Calculator and Excel® Manual. The videos walk students through algebraic solutions to pivotal examples and provide technological solutions where applicable. These videos are available to download from within MyMathLab®.

Enhanced and Updated:

• Section Previews have been updated and provide motivation for each section. Examples tied to these previews are now referenced in the Section Preview in the order in which they appear in the section.
• Skills Check andApplication Exercises have been increased significantly, especially in the new Chapters 1-4.
• Real data application examples and exercises have been updated, many new real data applications have been added, and more applied examples have been added to the exposition.
• MathXL®exercise coverage has been expanded to be as comparable as possible with more traditional texts.

Table of Contents

1. Functions, Graphs, and Models

            Algebra Toolbox

            Sets

            The Real Numbers

            Inequalities and Intervals on the Real Number Line

            Algebraic Expressions

            Polynomials

            Removing Parentheses

            The Coordinate System

            Subscripts

1.1 Functions and Models

            Function  Definitions

            Domains and Ranges

            Tests for Functions

            Functional Notation

            Mathematical Models

1.2 Graphs of Functions

            Graphs of Functions

            Graphing with Technology

            Aligning Data

            Determining Viewing windows

            Graphing Data Points

1.3 Linear Functions

            Linear Functions

            Intercepts

            Slope of a Line

            Slope and y-Intercept of a Line

            Constant Rate of Change

            Revenue, Cost, and Profit

            Special Linear Functions

1.4 Equations of Lines

            Writing Equations of Lines

            Vertical and Horizontal Lines

            Parallel and Perpendicular Lines

            Average Rate of Change

            Approximately Linear Data

            Summary

            Key Concepts and Formulas

            Chapter 1 Skills Check

            Chapter 1 Review Exercises

            Group Activity/ Extended Application

2. Linear Models, Equations and Inequalities

            Algebra Toolbox

            Properties of Equations

            Conditional Equations

            Identities

            Contradictions

            Properties of Inequalities

2.1   Algebraic and Graphical Solutions of Linear Equations

            Algebraic Solutions of Linear Equations

            Solutions, Zeros, and x-Intercepts

            Graphical Solution of Linear Equations

            Literal Equations; Solving an Equation for a Specified Linear Variable

            Direct Variation

2.2 Fitting Lines to Data Points: Modeling Linear Functions

            Exact and Approximate Linear Models

            Fitting Lines to Data Points; Linear Regression

            Applying Models

            Goodness of Fit

2.3 Systems of Linear Equations in Two Variables

            Graphical Solution of Systems

            Solution by Substitution

            Solution by Elimination

            Modeling Systems of Linear Equations

            Dependent and Inconsistent Systems

2.4 Solution of Linear Inequalities

            Algebraic Solution of Linear Inequalities

            Graphical Solution of Linear Inequalities

            Intersection Method

            x-Intercept Method

            Double Inequalities

            Summary

            Key Concepts and Formulas

            Chapter 2 Skills Check

            Chapter 2 Review Exercises

            Group Activity/ Extended Application

3. Quadratic and Other Nonlinear Functions

            Algebra Toolbox

            Integer exponents

            Absolute Value

            Rational exponents and radicals

            Multiplication of monomials and binomials

            Factoring

            Complex numbers

3.1 Quadratic Functions; Parabolas

            Parabolas

            Vertex Form of a Quadratic Function

3.2 Solving Quadratics Equations

            Factoring Methods

            Graphical Methods

            Combining Graphs and Factoring

            Graphical and Numerical Methods

            The Square Root Methods

            Completing the Square

            The Quadratic Formula

            The Discriminant

            Aids for Solving Quadratic Equations

            Equations with Complex Solutions

3.3 Piece-wise-Defined and Power Functions

            Piecewise-Defined Functions

            Absolute Value Function

            Solving Absolute Value Equations

            Power Functions

            Functions with Rational Exponents; Root Functions

            The Reciprocal Function

3.4 Quadratic and Power Models

            Modeling with Quadratic Functions

            Comparison of Quadratic and Linear Models

            Modeling with Power Functions

            Comparison of Power and Quadratic Models

            Summary

            Key Concepts and Formulas

            Chapter 3 Skills Check

            Chapter 3 Review Exercises

            Group Activity/ Extended Application

4. Additional Topics with Functions

            Algebra Toolbox

            Symmetry About the y-Axis

            Symmetry About the x-Axis

            Graphing Relations

            One-to-One Functions

4.1 Transformations of Graphs and Symmetry

            Shifts of Graphs of Functions

            Stretching and Compressing Graphs

            Reflections of Graphs

            Symmetry; Even and Odd Functions

4.2 Combining Functions; Composite Functions

            Operations with Functions

            Composition of Functions

4.3 Inverse Functions

            Inverse Functions

            Inverse Functions on Limited Domains

4.4 Additional Equations and Inequalities

            Radical Equations

            Equations with Rational Powers

            Quadratic Inequalities

            Power Inequalities

            Absolute Value Inequalities

            Summary

            Key Concepts and Formulas

            Chapter 4 Skills Check

            Chapter 4 Review Exercises

            Group Activity/ Extended Application

5. Exponential and Logarithmic Functions

            Algebra Toolbox

            Properties of Exponents

            Real Number Exponents

            Exponential Expressions

            Scientific Notation

5.1 Exponential Functions

            Exponential Functions

            Transformations of Graphs of Exponential Functions

            Exponential Growth

            Exponential Decay

            The Number e

5.2   Logarithmic Functions; Properties of Logarithms

            Logarithmic Functions

            Common Logarithms

            Natural Logarithms

            Logarithmic Properties

5.3  Exponential and Logarithmic Equations

            Solving Exponential Equations Using Logarithmic Forms

            Change of Base

            Solving Exponential Equations Using Logarithmic Properties

            Solution of Logarithmic Equations

            Exponential and Logarithmic Inequalities

5.4 Exponential and Logarithmic Models

            Modeling with Exponential Functions

            Constant Percent Change in Exponential Models

            Comparison of Models

            Logarithmic Models

            Exponents, Logarithms, and Linear Regression

5.5 Exponential Functions and Investing

            Compound Interest

            Continuous Compounding and the Number e

            Present Value of an Investment

            Investment Models

5.6 Annuities; Loan Repayment

            Future Value of an Annuity

            Present Value of an Annuity

            Loan Repayment

5.7 Logistic and Gompertz Functions

            Logistic Functions

            Gompertz Functions

            Summary

            Key Concepts and Formulas

            Chapter 5 Skills Check

            Chapter 5 Review Exercises

            Group Activity/ Extended Application

6. Higher-Degree Polynomial and Rational Functions

            Algebra Toolbox

            Polynomials

            Factoring Higher-Degree Polynomials

            Rational Expressions

            Multiplying and Dividing Rational Expressions

            Adding and Subtracting Rational Expressions

            Division of Polynomials

6.1 Higher -Degree Polynomial Functions

            Cubic Functions

            Quartic Functions

6.2 Modeling Cubic and Quartic Functions

            Modeling with Cubic Functions

            Modeling with Quartic Functions

            Model Comparisons

            Third and Fourth Differences

6.3 Solution of Polynomial Equations

            Solving Polynomial Equations by Factoring

            Solution Using Factoring by Grouping

            The Root Method

            Estimating Solutions with Technology

6.4 Polynomial Equations Continued; Fundamental Theorem of Algebra

            Division of Polynomials; Synthetic Division

            Using Division to Solve Cubic Equations

            Graphs and Solutions

            Rational Solutions Test

            Fundamental Theorem of Algebra

6.5 Rational Functions and Rational Equations

            Graphs of Rational Functions

            Analytic and Graphical Solution of Rational Equations

6.6 Polynomial and Rational Inequalities

            Polynomial Inequalities

            Rational Inequalities

            Summary

            Key Concepts and Formulas

            Chapter 6 Skills Check

            Chapter 6 Review Exercises

            Group Activity/ Extended Application

7. Systems of Equations and Inequalities; Matrices

            Algebra Toolbox

            Proportional Triples

            Linear Equations in Three Variables

            Systems of Three Equations in Three Variables

7.1 Systems of Linear Equations in Three Variables

            Systems in Three Variables

            Left-to-Right Elimination Method

            Modeling Systems of Equations

            Nonunique Solutions

7.2 Matrix Solution of Systems of Linear Equations

            Matrix Representation of Systems of Equations

            Echelon Forms of Matrices; Solving Systems with Matrices

            Gauss-Jordan Elimination

            Solution with Technology

            Nonunique Solution

            Dependent Systems

            Inconsistent Solutions

7.3 Matrix Operations

            Addition and Subtraction of Matrices

            Multiplication of a Matrix by a Number

            Matrix Multiplication

            Multiplication with Technology

7.4 Inverse Matrices; Matrix Equations

            Inverse Matrices

            Inverses and Technology

            Encoding and Decoding Messages

            Matrix Equations

            Matrix Equations and Technology

7.5  Systems of Nonlinear Equations

            Algebraic Solution of Nonlinear Systems

            Graphical Solution of Nonlinear Systems

            Summary

            Key Concepts and Formulas

            Chapter 7 Skills Check

            Chapter 7 Review Exercises

            Group Activity/ Extended Application

8. Special Topics

            Systems of Inequalities and Linear Programming

            Sequences and Series

            Preparing for Calculus

8.1 Systems of Inequalities

            Linear Inequalities in Two Variables

            Systems of Inequalities in Two Variables

8.2 Linear Programming: Graphical Methods

            Linear Programming

            Solution with Technology

8.3 Sequences and Discrete Functions

            Sequences

            Arithmetic Sequences

            Geometric Sequences

8.4 Series

            Finite and Infinite Series

            Arithmetic Series

            Geometric Series

            Infinite Geometric Series

8.5 Preparing for Calculus

            Chapter 1 Skills

            Chapter 2 Skills

            Chapter 3 Skills

            Chapter 4 Skills

            Chapter 5 Skills

            Chapter 6 Skills

            Summary

            Key Concepts and Formulas

            Chapter 8 Skills Check

            Chapter 8 Review Exercises

            Group Activity/ Extended Application

Appendix A. Basic Calculator Guide

Appendix B. Basic Excel Guide

Author

Ron Harshbarger got his BS from Shippensburg State, an MST from the University of New Hampshire, did graduate work at Penn State University, and received a PhD from the University of Pittsburgh. During a long and highly successful career at Penn State University, Dr. Harshbarger received both teaching and advising awards. At Georgia Southern University, he taught a wide variety of undergraduate and graduate courses in mathematics, developed five new mathematics courses, and created the mathematics component for a new doctoral degree.

At the University of South Carolina Beaufort, Dr. Harshbarger was named Professor of the year in 1999. In 2000, Professor Harshbarger was named the Governor's Professor of the Year for the State of South Carolina. In 2001, the University of South Carolina Board of Trustees named him the Trustee Professor of the Year. In 2002, he received the Mathematical Association of America Southeastern Section Award for Distinguished University Teaching of Mathematics. He was nominated for the 2003 Haimo Award for Distinguished College or University Teaching of Mathematics, a national award given by the Mathematical Association of America. In 2003, he was also named Professor of the Year at the University of South Carolina Beaufort and given the Governor's Distinguished Professor Award for the state of South Carolina.

Lisa Yocco received her undergraduate degree in mathematics from Augusta State University and her graduate degree in mathematics education from Florida State University. She has taught at both the college level and the high school level for twenty years, with her most recent experience at Georgia Southern University. She has co-authored several manuals in mathematics and graphing calculators and has presented workshops and papers at numerous conferences. In addition to her textbook writing and teaching, she enjoys spending time with her three children, cooking, and working on interior decorating.