College Algebra in Context

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.

Contents

Preface

List of Supplements

To the Student

1. Functions, Graphs, and Models; Linear Functions

            Algebra Toolbox

1.1 Functions and Models

1.2 Graphs of Functions

1.3 Linear Functions

1.4 Equations of Lines

            Summary

            Key Concepts and Formulas

            Chapter 1 Skills Check

            Chapter 1 Review

            Group Activities/Extended Applications

2. Linear Models, Equations, and Inequalities

            Algebra Toolbox

2.1 Algebraic and Graphical Solution of Linear Equations

2.2 Fitting Lines to Data Points: Modeling Linear Functions

2.3 Systems of Linear Equations in Two Variables

2.4 Solutions of Linear Inequalities

            Summary

            Key Concepts and Formulas

            Chapter 2 Skills Check

            Chapter 2 Review

            Group Activities/Extended Applications

3. Quadratic, Piecewise-Defined, and Power Functions

            Algebra Toolbox

3.1 Quadratic Functions; Parabolas

3.2 Solving Quadratic Equations

3.3 Piecewise-Defined Functions and Power Functions

3.4 Quadratic and Power Models

            Summary

            Key Concepts and Formulas

            Chapter 3 Skills Check

            Chapter 3 Review

            Group Activities/Extended Applications

4. Additional Topics with Functions

            Algebra Toolbox

4.1 Transformations of Graphs and Symmetry

4.2 Combining Functions; Composite Functions

4.3 One-to-One and Inverse Functions

4.4 Additional Equations and Inequalities

            Summary

            Key Concepts and Formulas

            Chapter 4 Skills Check

            Chapter 4 Review

            Group Activities/Extended Applications

5. Exponential and Logarithmic Functions

            Algebra Toolbox

5.1 Exponential Functions

5.2 Logarithmic Functions; Properties of Logarithms

5.3 Exponential and Logarithmic Equations

5.4 Exponential and Logarithmic Models

5.5 Exponential Functions and Investing

5.6 Annuities; Loan Repayment

5.7 Logistic and Gompertz Functions

            Summary

            Key Concepts and Formulas

            Chapter 5 Skills Check

            Chapter 5 Review

            Group Activities/Extended Applications

6. Higher-Degree Polynomial and Rational Functions

            Algebra Toolbox

6.1 Higher-Degree Polynomial Functions

6.2 Modeling with Cubic and Quartic Functions

6.3 Solution of Polynomial Equations

6.4 Polynomial Equations Continued; Fundamental Theorem of Algebra

6.5 Rational Functions and Rational Equations

6.6 Polynomial and Rational Inequalities

            Summary

            Key Concepts and Formulas

            Chapter 6 Skills Check

            Chapter 6 Review

            Group Activities/Extended Applications

7. Systems of Equations and Matrices

            Algebra Toolbox

7.1 Systems of Linear Equations in Three Variables

7.2 Matrix Solution of Systems of Linear Equations

7.3 Matrix Operations

7.4 Inverse Matrices; Matrix Equations

7.5 Systems of/onlinear Equations

            Summary

            Key Concepts and Formulas

            Chapter 7 Skills Check

            Chapter 7 Review

            Group Activities/Extended Applications

8. Special Topics: Systems of Inequalities and Linear Programming; Sequences and Series; Preparing for Calculus

8.1 Systems of Inequalities

8.2 Linear Programming: Graphical Methods

8.3 Sequences and Discrete Functions

8.4 Series

8.5 Preparing for Calculus

            Summary

            Key Concepts and Formulas

            Chapter 8 Skills Check

            Chapter 8 Review

            Group Activity/Extended Application

Appendix A:  Basic Calculator Guide

Appendix B:  Basic Guide to Excel 2003 and Excel 2010

Answers to Selected Exercises

Index

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