College Algebra Concepts Through Functions

Chapter F: Foundations – A Prelude to Functions

F.1 The Distance and Midpoint Formulas

F.3 Lines

F.4 Circles

Chapter 1: Functions and Their Graphs

1.1 Functions

1.2 The Graph of a Function

1.3 Properties of Functions

1.4 Library of Functions; Piecewise - defined  Functions

1.5 Graphing Techniques: Transformations

Chapter 2: Linear and Quadratic Functions

2.1 Properties of Linear Functions and Linear Models

2.3 Quadratic Functions and Their Zeros

2.4 Properties of Quadratic Functions

2.5 Inequalities Involving Quadratic Functions

2.6 Building Quadratic Models from Verbal Descriptions and from Data

2.8 Equations and Inequalities Involving the Absolute Value Function

Chapter 3: Polynomial and Rational Functions

3.1 Polynomial Functions and Models

3.2 The Real zeros of a Polynomial Function (omitting Descartes’ Rule of Signs and the Bounds on the Zeros theorem)

3.3 Complex zeros; Fundamental Theorem of Algebra

3.4 Properties a Rational Function

3.5 The Graph of a Rational Function

3.6 Polynomial and Rational Inequalities

Chapter 4: Exponential and Logarithmic Functions

4.1 Composite Functions

4.2 One-to-One Functions; Inverse Functions

4.3 Exponential Functions

4.4 Logarithmic Functions

4.5 Properties of Logarithms

4.6 Logarithmic and Exponential Equations

4.8 Exponential Growth and Decay Models

Chapter 6: Systems of Equations and Inequalities

6.2 Systems of Linear Equations: Matrices

Chapter 7: Sequences; Induction; the Binomial Theorem

7.1 Sequences

7.2 Arithmetic Sequences

7.3 Geometric Sequences; Geometric Series

7.5 The Binomial Theorem

Chapter A: Appendix

A.5 Synthetic Division

A.8 Solving Equations

A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs

A.10 Interval Notation; Solving Inequalities