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 Factoring Polynomials
R.6 Rational Expressions
1. Equations, Inequalities, and Applications
1.1 Linear Equations
1.2 Applications of Linear Equations
1.3 Complex Numbers
1.4 Quadratic Equations
1.5 Applications of Quadratic Equations
1.6 Other Types of Equations
1.7 Linear Inequalities
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 The Natural Exponential Function
5.3 Logarithmic Functions
5.4 Properties of Logarithms
5.5 Exponential and Logarithmic Equations
5.6 Applications of Exponential and Logarithmic Functions
6. Conic Sections
6.1 The Parabola
6.2 The Ellipse
6.3 The Hyperbola
7. Systems of Equations and Inequalities
7.1 Systems of Linear Equations in Two Variables
7.2 Systems of Linear Equations in Three Variables
7.3 Inconsistent and Dependent Linear Systems in Three Variables
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 A. Conic Section Proofs