College Algebra: Graphs & Models
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College Algebra: Graphs & Models

Chapter R: A Review of Basic Concepts and Skills

R.1: Algebraic Expressions and the Properties of Real Numbers

R.2: Exponents, Scientific Notation, and a Review of Polynomials

R.3: Solving Linear Equations and Inequalities

R.4: Factoring Polynomials and Solving Polynomial Equations by Factoring

R.5: Rational Expressions and Equations

R.6: Radicals, Rational Exponents, and Radical Equations

Chapter 1: Functions and Graphs

1.1: Rectangular Coordinates, Graphing Circles and Other Relations

1.2: Functions, Function Notation, and the Graph of a Function

1.3: Linear Equations and Rates of Change

1.4: Linear Functions, Special Forms, and More on Rates of Change

1.5: Solving Equations and Inequalities Graphically; Formulas and Problem Solving

1.6: Linear Models and Real Data

Chapter 2: Relations, More on Functions

2.1: Analyzing the Graph of a Function

2.2: The Toolbox Functions and Transformations

2.3: Absolute Value Functions, Equations, and Inequalities

2.4: Rational and Radical Functions; More on the Domain

2.5: Piecewise-Defined Functions

2.6: Variation: The Toolbox Functions in Action

Chapter 3: Quadratic Functions and Operations on Functions

3.1: Complex Numbers

3.2: Solving Quadratic Equations and Inequalities

3.3: Quadratic Functions and Applications

3.4: Quadratic Models; More on Rates of Change

3.5: The Algebra of Functions

3.6: Composition of Functions and the Difference Quotient

Chapter 4: Polynomial and Rational Functions

4.1: Synthetic Division; the Remainder and Factor Theorems

4.2: The Zeros of Polynomial Functions

4.3: Graphing Polynomial Functions

4.4: Graphing Rational Functions

4.5: Additional Insights into Rational Functions

Chapter 5: Exponential and Logarithmic Functions

5.1: One-to-One and Inverse Functions

5.2: Exponential Functions

5.3: Logarithms and Logarithmic Functions

5.4: Properties of Logarithms

5.5: Solving Exponential/Logarithmic Equations

5.6: Applications from Business, Finance, and Science

5.7: Exponential, Logarithmic, and Logistic Equation Models

Chapter 6: Systems of Equations and Inequalities

6.1: Linear Systems in Two Variables with Applications

6.2: Linear Systems in Three Variables with Applications

6.3: Nonlinear Systems of Equations and Inequalities

6.4: Systems of Inequalities and Linear Programming

Chapter 7: Matrices and Matrix Applications

7.1: Solving Linear Systems Using Matrices and Row Operations

7.2: The Algebra of Matrices

7.3: Solving Linear Systems Using Matrix Equations

7.4: Applications of Matrices and Determinants: Cramer’s rule, Partial Fractions, and More

7.5: Matrix Applications and Technology Use

Chapter 8: Analytic Geometry and the Conic Sections

8.1: A Brief Introduction to Analytic Geometry

8.2: The Circle and the Ellipse

8.3: The Hyperbola

8.4: The Analytic Parabola: More on Nonlinear Systems

Chapter 9: Additional Topics in Algebra

9.1: Sequences and Series

9.2: Arithmetic Sequences

9.3: Geometric Sequences

9.4: Mathematical Induction

9.5: Counting Techniques

9.6: Introduction to Probability

9.7: The Binomial Theorem


The Language, Notation, and Numbers of Mathematics

Geometry Review with Unit Conversions

More on Synthetic Division

More on Matrices

Deriving the Equation of a Conic

Proof Positive - A Selection of Proofs from College Algebra