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College Algebra in Context with Applications for the Managerial, Life, and Social Sciences / Edition 3

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Overview

KEY BENEFIT: Harshbarger/Yocco’s College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, Third Edition uses modeling and real-data problems to develop the skills that readers will need for their future courses and careers. Applications anticipate the math that readers will encounter in their professional lives, giving them the practice they need to become adept problem-solvers. Every chapter begins with the Algebra Toolbox, which reviews the skills and concepts necessary to master the material ahead. This new full-color edition offers a greater number of technology tips, and the content has been reorganized to accommodate a wide range of course syllabi.

KEY TOPICS: Functions, Graphs, and Models; Linear Models, Equations and Inequalities; Quadratic and Other Nonlinear Functions; Additional Topics with Functions; Exponential and Logarithmic Functions; Higher-Degree Polynomial and Rational Functions; Systems of Equations and Inequalities; Matrices; Special Topics

MARKET: For all readers interested in college algebra.

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Product Details

  • ISBN-13: 9780321570604
  • Publisher: Pearson
  • Publication date: 1/15/2009
  • Edition description: Older Edition
  • Edition number: 3
  • Pages: 768
  • Product dimensions: 8.70 (w) x 10.00 (h) x 1.20 (d)

Meet the 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.

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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

Answers to Selected Exercises

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