Elementary and Intermediate Algebra Graphs and Models

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts—Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.

Barbara Johnson has a B.S. in mathematics from Bob Jones University and a M.S. in math from Clemson University. She has taught high school and college math for 25 years, and enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics.  As a Purdue Master Gardener, she also enjoys helping others learn gardening skills.  Believing that the best teacher is always learning, she recently earned a black belt in karate.

Preface

1. Introduction to Algebraic Expressions
1.1 Introduction to Algebra Models
1.2 The Commutative, Associative, and Distributive Laws
1.3 Fraction Notation
1.4 Positive and Negative Real Numbers
Mid-Chapter Review
1.5 Addition of Real Numbers
1.6 Subtraction of Real Numbers
1.7 Multiplication and Division of Real Numbers
1.8 Exponential Notation and Order of Operations

2. Equations, Inequalities, and Problem Solving
2.1 Solving Equations
2.2 Using the Principles Together
2.3 Formulas
Mid-Chapter Review
2.4 Applications with Percent
2.5 Problem Solving
2.6 Solving Inequalities
2.7 Solving Applications with Inequalities

3. Introduction to Graphing and Functions
3.1 Reading Graphs, Plotting Points, and Scaling Graphs
3.2 Graphing Equations
3.3 Linear Equations and Intercepts
3.4 Rates
3.5 Slope
Mid-Chapter Review
3.6 Slope-Intercept Form
3.7 Point-Slope Form; Introduction to Curve
3.8 Functions

4. Systems of Equations in Two Variables
4.1 Systems of Equations and Graphing
Solutions of Systems
4.2 Systems of Equations and Substitution
4.3 Systems of Equations and Elimination
Mid-Chapter Review
4.4 More Applications Using Systems
4.5 Solving Equations by Graphing

5. Polynomials
5.1 Exponents and Their Properties
5.2 Negative Exponents and Scientific Notation
5.3 Polynomials and Polynomial Functions
5.4 Addition and Subtraction of Polynomials
5.5 Multiplication of Polynomials
5.6 Special Products
Mid-Chapter Review
5.7 Polynomials in Several Variables
5.8 Division of Polynomials
5.9 The Algebra of Functions

6. Polynomial Factorizations and Equations
6.1 Introduction to Polynomial Factorizations and Equations
6.2 Trinomials of the Type x ² + bx + c
6.3 Trinomials of the Type ax ² + bx + c
Mid-Chapter Review
6.4 Perfect-Square Trinomials and Differences of Squares
6.5 Sums or Differences of Cubes
6.6 Factoring: A General Strategy
6.7 Applications of Polynomial Equations
Cumulative Review: Chapters 1-6

7. Rational Expressions, Equations, and Functions
7.1 Rational Expressions and Functions
7.2 Multiplication and Division
7.3 Addition, Subtraction, and Least Common Denominators
7.4 Addition and Subtraction with Unlike Denominators
Mid-Chapter Review
7.5 Complex Rational Expressions
7.6 Rational Equations
7.7 Applications Using Rational Equations and Proportions
7.8 Formulas, Applications, and Variation

8. Inequalities
8.1 Graphical Solutions and Compound Inequalities
8.2 Absolute-Value Equations and Inequalities
Mid-Chapter Review
8.3 Inequalities in Two Variables
8.4 Polynomial Inequalities and Rational Inequalities

9. More on Systems
9.1 Systems of Equations in Three Variables
9.2 Solving Applications: Systems of Three Equations
9.3 Elimination Using Matrices
Mid-Chapter Review
9.4 Determinants and Cramer's Rule
9.5 Business and Economics Applications
Cumulative Review: Chapters 1-9

10. Exponents and Radical Functions
10.1 Radical Expressions, Functions, and Models
10.2 Rational Numbers as Exponents
10.3 Multiplying Radical Expressions
10.4 Dividing Radical Expressions
10.5 Expressions Containing Several Radical Terms
Mid-Chapter Review
10.6 Solving Radical Equations
10.7 The Distance Formula, the Midpoint Formula, and Other Applications
10.8 The Complex Numbers

11. Quadratic Functions and Equations
11.1 Quadratic Equations
11.2 The Quadratic Formula
11.3 Studying Solutions of Quadratic Equations
11.4 Applications Involving Quadratic Equations
11.5 Equations Reducible to Quadratic
Mid-Chapter Review
11.6 Quadratic Functions and Their Graphs
11.7 More About Graphing Quadratic Functions
11.8 Problem Solving and Quadratic Functions

12. Exponential Functions and Logarithmic Functions
12.1 Composite Functions and Inverse Functions
12.2 Exponential Functions
12.3 Logarithmic Functions
12.4 Properties of Logarithmic Functions
Mid-Chapter Review
12.5 Natural Logarithms and Changing Bases
12.6 Solving Exponential and Logarithmic Equations
12.7 Applications of Exponential and Logarithmic Functions
Cumulative Review Chapters 1-12

13. Conic Sections
13.1 Conic Sections: Parabolas and Circles
13.2 Conic Sections: Ellipses
13.3 Conic Sections: Hyperbolas
Mid-Chapter Review
13.4 Nonlinear Systems of Equations

14. Sequences, Series, and the Binomial Theorem
14.1 Sequences and Series
14.2 Arithmetic Sequences and Series
14.3 Geometric Sequences and Series
Mid-Chapter Review
14.4 The Binomial Theorem
Cumulative Review: Chapters 1-14

R. Elementary Algebra Review
R.1 Introduction to Algebraic Expressions
R.2 Equations, Inequalities, and Problem Solving
R.3 Introduction to Graphing and Functions
R.4 Systems of Equations in Two Variables
R.5 Polynomials
R.6 Polynomial Factorizations and Equations

Answers
Glossary
Photo Credits
Index
Index of Applications