# Intermediate Algebra

**by**Bittinger, Marvin L.

### 9780321613363

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## Summary

## Author Biography

**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.

## Table of Contents

**Chapter R Review of Basic Algebra**

Part 1 Operations

R.1 The Set of Real Numbers

R.2 Operations with Real Numbers

R.3 Exponential Notation and Order of Operations

Part 2 Manipulations

R.4 Introduction to Algebraic Expressions

R.5 Equivalent Algebraic Expressions

R.6 Simplifying Algebraic Expressions

R.7 Properties of Exponents and Scientific Notation

**Chapter 1 Solving Linear Equations and Inequalities**

1.1 Solving Equations

1.2 Formulas and Applications

1.3 Applications and Problem Solving

1.4 Sets, Inequalities, and Interval Notation

1.5 Intersections, Unions, and Compound Inequalities

1.6 Absolute-Value Equations and Inequalities

**Chapter 2 Graphs, Functions, and Applications**

2.1 Graphs of Equations

2.2 Functions and Graphs

2.3 Finding Domain and Range

2.4 Linear Functions: Graphs and Slope

2.5 More on Graphing Linear Equations

2.6 Finding Equations of Lines: Applications

**Chapter 3 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

3.5 Systems of Equations in Three Variables

3.6 Solving Applied Problems: Three Equations

3.7 Systems of Inequalities in Two Variables

**Chapter 4 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: *x ^{2} *+

*bx*+

*c*

4.5 Factoring Trinomials: *ax ^{2} * +

*bx*+

*c*,

*a ≠*1

4.6 Special Factoring

4.7 Factoring: A General Strategy

4.8 Applications of Polynomial Equations and Functions

**Chapter 5 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

5.5 Solving Rational Equations

5.6 Applications and Proportions

5.7 Formulas and Applications

5.8 Variation and Applications

**Chapter 6 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

6.5 More on Division of Radical Expressions

6.6 Solving Radical Equations

6.7 Applications Involving Powers and Roots

6.8 The Complex Numbers

**Chapter 7 Quadratic Equations and Functions**

7.1 The Basics of Solving Quadratic Equations

7.2 The Quadratic Formula

7.3 Applications Involving Quadratic Equations

7.4 More on Quadratic Equations

7.5 Graphing *f(x) = a(x – h) ^{2} + k*

7.6 Graphing *f(x) = ax ^{2} + bx + c*

7.7 Mathematical Modeling with Quadratic Functions

7.8 Polynomial and Rational Inequalities

**Chapter 8 Exponential and Logarithmic Functions**

8.1 Exponential Functions

8.2 Inverse and Composite Functions

8.3 Logarithmic Functions

8.4 Properties of Logarithmic Functions

8.5 Natural Logarithmic Functions

8.6 Solving Exponential and Logarithmic Equations

8.7 Mathematical Modeling with Exponential and Logarithmic Functions

**Chapter 9 Conic Sections**

9.1 Parabolas and Circles

9.2 Ellipses

9.3 Hyperbolas

9.4 Nonlinear Systems of Equations

**Appendices **

A. Handling Dimension Symbols

B. Determinants and Cramer’s Rule

C. Elimination Using Matrices

D. The Algebra of Functions