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Table of Contents

1 Introduction to Functions and Graphs

R Review

1. Numbers, Data, and Problem Solving
2. Visualizing and Graphing Data
3. Functions and Their Representations
4. Types of Functions and Their Rates of Change

2 Linear Functions and Equations

R Review

1. Equations of Lines
2. Linear Equations
3. Linear Inequalities
4. More Modeling with Functions
5. Absolute Value Equations and Inequalities

3 Quadratic Functions and Equations

R Review

1. Quadratic Functions and Models
2. Quadratic Equations and Problem Solving
3. Complex Numbers
4. Quadratic Inequalities
5. Transformations of Graphs

4 More Nonlinear Functions and Equations

R Review

1. More Nonlinear Functions and Their Graphs
2. Polynomial Functions and Models
3. Division of Polynomials
4. Real Zeros of Polynomial Functions
5. The Fundamental Theorem of Algebra
6. Rational Functions and Models
7. More Equations and Inequalities
8. Radical Equations and Power Functions

5 Exponential and Logarithmic Functions

R Review

1. Combining Functions
2. Inverse functions and Their Representations
3. Exponential Functions and Models
4. Logarithmic Functions and Models
5. Properties of Logarithms
6. Exponential and Logarithmic Equations
7. Constructing Nonlinear Models

6 Systems of Equations and Inequalities

R Review

1. Functions and Systems of Equations in Two Variables
2. Systems of Inequalities in Two Variables
3. Systems of Linear Equations in Three Variables
4. Solutions to Linear Systems Using Matrices
5. Properties and Applications of Matrices
6. Inverses of Matrices
7. Determinants

7 Conic Sections

1. Parabolas
2. Ellipses
3. Hyperbolas

8 Further Topics in Algebra

R Review

1. Sequences
2. Series
3. Counting
4. The Binomial Theorem
5. Mathematical Induction
6. Probability

R Reference: Basic Concepts from Algebra and Geometry

1. Formulas from Geometry
2. Integer Exponents
3. Polynomial Expressions
4. Factoring Polynomials
5. Rational Expressions
6. Radical Notation and Rational Exponents
7. Radical Expressions

Appendices

Appendix A: Using the Graphing Calculator, no exercises necessary

Appendix B: A Library of Functions, no exercises necessary

Appendix C: Partial Fractions

Appendix D: Percent Change and Exponential Functions

 

Get College Algebra with Integrated Review plus MyLab Math Student Access Card and Worksheets by Gary K. Rockswold, Minnesota State University, Mankato

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