BRIEF TABLE OF CONTENTS:

Review Chapter

1. Equations, Inequalities, and Applications

2. The Rectangular Coordinate System, Lines, and Circles

3. Functions

4. Polynomial and Rational Functions

5. Exponential and Logarithmic Functions and Equations

6. Conic Sections and Parametric Equations

7. Systems of Equations and Inequalities

8. Matrices

9. Sequences and Series; Counting and Probability

Appendix: Conic Section Proofs

COMPREHENSIVE TABLE OF CONTENTS:

Review Chapter

R.1 Real Numbers

R.2 The Order of Operations and Algebraic Expressions

R.3 The Laws of Exponents; Radicals

R.4 Polynomials

R.5 Operations with Radicals (New Section)

R.6 Factoring Polynomials

R.7 Rational Expressions

1. Equations, Inequalities, and Applications

1.1 Linear and Rational Equations

1.2 Applications of Linear Equations and Rational Equation

1.3 Complex Numbers

1.4 Quadratic Equations

1.5 Applications of Quadratic Equations

1.6 Other Types of Equations

1.7 Linear Inequalities in One Variable

1.8 Absolute Value Equations and Inequalities

1.9 Polynomial and Rational Inequalities

2. The Rectangular Coordinate System, Lines, and Circles

2.1 The Rectangular Coordinate System

2.2 Circles

2.3 Lines

2.4 Parallel and Perpendicular Lines

3. Functions

3.1 Relations and Functions

3.2 Properties of a Function's Graph

3.3 Graphs of Basic Functions; Piecewise Functions

3.4 Transformations of Functions

3.5 The Algebra of Functions; Composite Functions

3.6 One-to-One Functions; Inverse Functions

4. Polynomial and Rational Functions

4.1 Quadratic Functions

4.2 Applications and Modeling of Quadratic Functions

4.3 The Graphs of Polynomial Functions

4.4 Synthetic Division; The Remainder and Factor Theorems

4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra

4.6 Rational Functions and Their Graphs

4.7 Variation

5. Exponential and Logarithmic Functions and Equations

5.1 Exponential Functions

5.2 Logarithmic Functions

5.3 Properties of Logarithms

5.4 Exponential and Logarithmic Equations

5.5 Applications of Exponential and Logarithmic Functions

6. Conic Sections and Parametric Equations

6.1 Introduction to Conic Sections

6.2 The Parabola

6.3 The Ellipse
6.4 The Hyperbola

7. Systems of Equations and Inequalities

7.1 Solving Systems of Linear Equations in Two Variables

7.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method

7.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination

7.4 Partial Fraction Decomposition

7.5 Systems of Nonlinear Equations

7.6 Systems of Inequalities

8. Matrices

8.1 Matrix Operations

8.2 Inverses of Matrices and Matrix Equations

8.3 Determinants and Cramer's Rule

9. Sequences and Series; Counting and Probability

9.1 Introduction to Sequences and Series

9.2 Arithmetic Sequences and Series

9.3 Geometric Sequences and Series

9.4 The Binomial Theorem

9.5 Mathematical Induction

9.6 The Theory of Counting

9.7 An Introduction to Probability

Appendix: Conic Section Proofs

College Algebra, 4th edition

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