Intermediate Algebra

About our authors Marvin Bittinger has been teaching math at the university level for more than 38 years. Since 1968, he has been employed at Indiana University - Purdue University Indianapolis (IUPUI) 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. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." He also has an interest in philosophy and theology, particularly apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has 2 grown and married sons, Lowell and Chris, and 4 granddaughters. Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University - Purdue University Indianapolis (IUPUI). In addition to her career in textbook publishing, she enjoys traveling, spending time with her grandchildren and promoting charity projects for a children's camp. Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in mathematics from Clemson University, and is a PhD candidate in Educational Studies at Ball State University. She has taught high school and college math for 30 years, and she 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 is also a student of karate.

Index of Activities
Index of Animations
Preface
Index of Applications
JUST-IN-TIME REVIEW

The Set of Real Numbers
Order for the Real Numbers
Graphing Inequalities on the Number Line
Absolute Value
Add Real Numbers
Opposites, or Additive Inverses
Subtract Real Numbers
Multiply Real Numbers
Divide Real Numbers
Exponential Notation (Part 1)
Order of Operations
Translate to an Algebraic Expression
Evaluate Algebraic Expressions
Equivalent Fraction Expressions
The Commutative Laws and the Associative Laws
The Distributive Laws
Collecting Like Terms
Removing Parentheses and Collecting Like Terms
Exponential Notation (Part 2)
Scientific Notation





SOLVING LINEAR EQUATIONS AND INEQUALITIES

1.1 Solving Equations
1.2 Formulas and Applications
1.3 Applications and Problem Solving

Mid-Chapter Review


1.4 Sets, Inequalities, and Interval Notation

Translating for Success


1.5 Intersections, Unions, and Compound Inequalities
1.6 Absolute-Value Equations and Inequalities
Summary and Review
Test


GRAPHS, FUNCTIONS, AND APPLICATIONS

2.1 Graphs of Equations
2.2 Functions and Graphs
2.3 Finding Domain and Range

Mid-Chapter Review


2.4 Linear Functions: Graphs and Slope
2.5 More on Graphing Linear Equations

Visualizing for Success


2.6 Finding Equations of Lines; Applications
Summary and Review
Test
Cumulative Review


SYSTEMS OF EQUATIONS

3.1 Systems of Equations in Two Variables
3.2 Solving by Substitution
3.3 Solving by Elimination
3.4 Solving Applied Problems: Two Equations Translating for Success

Mid-Chapter Review


3.5 Systems of Equations in Three Variables
3.6 Solving Applied Problems: Three Equations
3.7 Systems of Inequalities in Two Variables
Visualizing for Success
Summary and Review
Test
Cumulative Review


POLYNOMIALS AND POLYNOMIAL FUNCTIONS

4.1 Introduction to Polynomials and Polynomial Functions
4.2 Multiplication of Polynomials
4.3 Introduction to Factoring
4.4 Factoring Trinomials: x2 + bx + c

Mid-Chapter Review


4.5 Factoring Trinomials: ax2 + bx + c, a ≠1
4.6 Special Factoring

Visualizing for Success


4.7 Factoring: A General Strategy
4.8 Applications of Polynomial Equations and Functions
Translating for Success
Summary and Review
Test
Cumulative Review


RATIONAL EXPRESSIONS, EQUATIONS, AND FUNCTIONS

5.1 Rational Expressions and Functions: Multiplying, Dividing, and Simplifying
5.2 LCMs, LCDs, Addition, and Subtraction
5.3 Division of Polynomials
5.4 Complex Rational Expressions

Mid-Chapter Review


5.5 Solving Rational Equations
5.6 Applications and Proportions

Translating for Success


5.7 Formulas and Applications
5.8 Variation and Applications
Summary and Review
Test
Cumulative Review


RADICAL EXPRESSIONS, EQUATIONS, AND FUNCTIONS

6.1 Radical Expressions and Functions
6.2 Rational Numbers as Exponents
6.3 Simplifying Radical Expressions
6.4 Addition, Subtraction, and More Multiplication

Mid-Chapter Review


6.5 More on Division of Radical Expressions
6.6 Solving Radical Equations
6.7 Applications Involving Powers and Roots

Translating for Success


6.8 The Complex Numbers
Summary and Review
Test
Cumulative Review


QUADRATIC EQUATIONS AND FUNCTIONS

7.1 The Basics of Solving Quadratic Equations
7.2 The Quadratic Formula
7.3 Applications Involving Quadratic Equations

Translating for Success


7.4 More on Quadratic Equations

Mid-Chapter Review


7.5 Graphing f(x) = a(x - h)2 + k
7.6 Graphingf(x) = a x2 + bx + c

Visualizing for Success


7.7 Mathematical Modeling with Quadratic Functions
7.8 Polynomial Inequalities and Rational Inequalities
Summary and Review
Test
Cumulative Review


EXPONENTIAL FUNCTIONS AND LOGARITHMIC FUNCTIONS

8.1 Exponential Functions
8.2 Composite Functions and Inverse Functions
8.3 Logarithmic Functions
8.4 Properties of Logarithmic Functions

Mid-Chapter Review


8.5 Natural Logarithmic Functions

Visualizing for Success


8.6 Solving Exponential Equations and Logarithmic Equations
8.7 Mathematical Modeling with Exponential Functions and Logarithmic Functions
Translating for Success
Summary and Review
Test
Cumulative Review


CONIC SECTIONS

9.1 Parabolas and Circles
9.2 Ellipses

Mid-Chapter Review


9.3 Hyperbolas

Visualizing for Success


9.4 Nonlinear Systems of Equations
Summary and Review
Test
Cumulative Review



APPENDIXES

Fraction Notation
Determinants and Cramer’s Rule
Elimination Using Matrices
The Algebra of Functions



Answers
Guided Solutions
Glossary
Index