## Table of Contents

**1. Linear Functions, Equations, and Inequalities**

1.1 Real Numbers and the Rectangular Coordinate System

1.2 Introduction to Relations and Functions

1.3 Linear Functions

1.4 Equations of Lines and Linear Models

1.5 Linear Equations and Inequalities

1.6 Applications of Linear Functions

**2. Analysis of Graphs of Functions**

2.1 Graphs of Basic Functions and Relations; Symmetry

2.2 Vertical and Horizontal Shifts of Graphs

2.3 Stretching, Shrinking, and Reflecting Graphs

2.4 Absolute Value Functions

2.5 Piecewise-Defined Functions

2.6 Operations and Composition

**3. Polynomial Functions**

3.1 Complex Numbers

3.2 Quadratic Functions and Graphs

3.3 Quadratic Equations and Inequalities

3.4 Applications of Quadratic Functions and Models

3.5 Higher-Degree Polynomial Functions and Graphs

3.6 Topics in the Theory of Polynomial Functions (I)

3.7 Topics in the Theory of Polynomial Functions (II)

3.8 Polynomial Equations and Inequalities; Further Applications and Models

**4. Rational, Power, and Root Functions**

4.1 Rational Functions and Graphs (I)

4.2 Rational Functions and Graphs (II)

4.3 Rational Equations, Inequalities, Models, and Applications

4.4 Functions Defined by Powers and Roots

4.5 Equations, Inequalities, and Applications Involving Root Functions

**5. Inverse, Exponential, and Logarithmic Functions**

5.1 Inverse Functions

5.2 Exponential Functions

5.3 Logarithms and Their Properties

5.4 Logarithmic Functions

5.5 Exponential and Logarithmic Equations and Inequalities

5.6 Further Applications and Modeling with Exponential and Logarithmic Functions

**6. Systems and Matrices**

6.1 Systems of Equations

6.2 Solution of Linear Systems in Three Variables

6.3 Solution of Linear Systems by Row Transformations

6.4 Matrix Properties and Operations

6.5 Determinants and Cramer’s Rule

6.6 Solution of Linear Systems by Matrix Inverses

6.7 Systems of Inequalities and Linear Programming

6.8 Partial Fractions

**7. Analytic Geometry and Nonlinear Systems**

7.1 Circles and Parabolas

7.2 Ellipses and Hyperbolas

7.3 The Conic Sections and Nonlinear Systems

7.4 Parametric Equations

**8. Further Topics in Algebra**

8.1 Sequences and Series

8.2 Arithmetic Sequences and Series

8.3 Geometric Sequences and Series

8.4 Counting Theory

8.5 The Binomial Theorem

8.6 Mathematical Induction

8.7 Probability

**R. Reference: Basic Algebraic Concepts**

R.1 Review of Exponents and Polynomials

R.2 Review of Factoring

R.3 Review of Rational Expressions

R.4 Review of Negative and Rational Exponents

R.5 Review of Radicals