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Table of Contents
- Chapter 1 • Functions and Inequalities
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Chapter 2 • Matrices
- Types of Matrices
- Adding and Subtracting Matrices
- Matrix Operations
- Scalar Multiplication of Matrices
- Matrix Multiplication
- Properties of Matrix Multiplication
- Two-by-Two Determinants
- Three-by-Three Determinants
- Using Determinants to Calculate Areas
- Cramer’s Rule
- Inverse of a 2 × 2 Matrix
- Solving a System of Two Equations Using a Matrix Inverse
-
Chapter 3 • Polynomials and Polynomial Functions
- Introduction to Complex Numbers
- Pure Imaginary Numbers
- Equating, Adding, and Subtracting Complex Numbers
- Complex Number Conjugates
- Multiplying Complex Numbers
- Simplifying Expressions: Rules of Exponents
- Solving Quadratic Equations: Quadratic Formula
- Discriminants of Quadratics
- Identifying Polynomials
- Simplifying Expressions: Combining Like Terms
- Dividing Polynomials by Monomials
- Polynomial Long Division without Remainder
- Graphs of Polynomial Functions
- Polynomial Functions
- Degree and Coefficient of Polynomials
- Polynomial Equations
- Polynomial Long Division with Remainder
- Remainder and Factor Theorem with Synthetic Division
- Solving Quadratic Equations with Complex Roots
- Real and Complex Roots of Polynomials
- Descartes’ Rule of Signs
- Forming a Quadratic Equation from its Roots
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Chapter 4 • Inverses and Radical Functions and Relations
- Combining Functions
- Composite Functions
- Graphs of Inverses of Functions
- Inverse of a Function
- Radical Functions
- Simplifying Radicals
- Approximating Radicals
- Adding and Subtracting Radical Expressions
- Rationalizing Denominators of Radicals
- Squares of Numbers
- Cubes of Numbers
- Fractional Exponents
- Radical Equations