Table of Contents

Table of Contents

R. Review of Basic Concepts

R-1 Fractions, Decimals, and Percents

R-2 Sets and Real Numbers

R-3 Real Number Operations and Properties

R-4 Integer and Rational Exponents

R-5 Polynomials

R-6 Factoring Polynomials

R-7 Rational Expressions

R-8 Radical Expressions

1. Equations and Inequalities

1-1 Linear Equations

1-2 Applications and Modeling with Linear Equations

1-3 Complex Numbers

1-4 Quadratic Equations

1-5 Applications and Modeling with Quadratic Equations

1-6 Other Types of Equations and Applications

1-7 Inequalities

1-8 Absolute Value Equations and Inequalities

2. Graphs and Functions

2-1 Rectangular Coordinates and Graphs

2-2 Circles

2-3 Functions

2-4 Linear Functions

2-5 Equations of Lines and Linear Models

2-6 Graphs of Basic Functions

2-7 Graphing Techniques

2-8 Function Operations and Composition

3. Polynomial and Rational Functions

3-1 Quadratic Functions and Models

3-2 Synthetic Division

3-3 Zeros of Polynomial Functions

3-4 Polynomial Functions: Graphs, Applications, and Models

3-5 Rational Functions: Graphs, Applications, and Models

3-6 Polynomial and Rational Inequalities

4. Inverse, Exponential, and Logarithmic Functions

4-1 Inverse Functions

4-2 Exponential Functions

4-3 Logarithmic Functions

4-4 Evaluating Logarithms and the Change-of-Base Theorem

4-5 Exponential and Logarithmic Equations

4-6 Applications and Models of Exponential Growth and Decay

5. Systems and Matrices

5-1 Systems of Linear Equations

5-2 Matrix Solution of Linear Systems

5-3 Determinant Solution of Linear Systems

5-4 Partial Fractions

5-5 Nonlinear Systems of Equations

5-6 Systems of Inequalities and Linear Programming

5-7 Properties of Matrices

5-8 Matrix Inverses

6. Analytic Geometry

6-1 Parabolas

6-2 Ellipses

6-3 Hyperbolas

6-4 Summary of the Conic Sections

7. Further Topics in Algebra

7-1 Sequences and Series

7-2 Arithmetic Sequences and Series

7-3 Geometric Sequences and Series

7-4 The Binomial Theorem

7-5 Mathematical Induction

7-6 Counting Theory

7-7 Basics of Probability

Answers to Selected Exercises

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