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More About This Textbook
Overview
KEY BENEFIT: Harshbarger/Yocco’s College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, Third Edition uses modeling and realdata 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 problemsolvers. Every chapter begins with the Algebra Toolbox, which reviews the skills and concepts necessary to master the material ahead. This new fullcolor 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; HigherDegree Polynomial and Rational Functions; Systems of Equations and Inequalities; Matrices; Special Topics
MARKET: For all readers interested in college algebra.
Product Details
Related Subjects
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 coauthored 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.
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 yIntercept 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 xIntercepts
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
xIntercept 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 PiecewiseDefined and Power Functions
PiecewiseDefined 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 yAxis
Symmetry About the xAxis
Graphing Relations
OnetoOne 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. HigherDegree Polynomial and Rational Functions
Algebra Toolbox
Polynomials
Factoring HigherDegree 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
LefttoRight 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
GaussJordan 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