Real Numbers and the Rectangular Coordinate System

Introduction to Relations and Functions

Linear Functions

Equations of Lines and Linear Models

Linear Equations and Inequalities

Applications of Linear Functions

Graphs of Basic Functions and Relations; Symmetry

Vertical and Horizontal Shifts of Graphs

Stretching, Shrinking, and Reflecting Graphs

Absolute Value Functions: Graphs, Equations, Inequalities, and Applications

Piecewise-Defined Functions

Operations and Composition

Complex Numbers

Quadratic Functions and Graphs

Quadratic Equations and Inequalities

Further Applications of Quadratic Functions and Models

Higher-Degree Polynomial Functions and Graphs

Topics in the Theory of Polynomial Functions (I)

Topics in the Theory of Polynomial Functions (II)

Polynomial Equations and Inequalities; Further Applications and Models

Rational Functions and Graphs

More on Graphs of Rational Functions

Rational Equations, Inequalities, Applications, and Models

Functions Defined by Powers and Roots

Equations, Inequalities, and Applications Involving Root Functions

Inverse Functions

Exponential Functions

Logarithms and Their Properties

Logarithmic Functions

Exponential and Logarithmic Equations and Inequalities

Further Applications and Modeling with Exponential Logarithmic Functions

Systems of Equations

Solution of Linear Systems in Three Variables

Solution of Linear Systems by Row Transformations

Matrix Properties and Operations

Determinants and Cramer's Rule

Solution of Linear Systems by Matrix Inverses

Systems of Inequalities and Linear Programming

Partial Fractions