Course: College Algebra
Topic: Functions and Graphs
Subtopic: Properties of Functions


Functions and graphs form the foundation of this course. You should already be very familiar with what a function is and how to determine if your have a function given data in the form of a set of ordered pairs, mapping, graph, or equation. Our goal in this class is to expand on that basic information and concentrate on properties of functions, learn several important new terms, study various features of functions and their graphs, analyze the information obtained from a graph, and use this information in practical applications.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: function, vertical line test (VLT), domain, range, symmetry, symmetry test, even function, odd function, increasing function, decreasing function, constant function, local (a.k.a. relative) minimum/maximum point, absolute minimum/maximum value, extrema point, extrema value

Mini-Lectures and Examples

STUDY: Functions - Properties, Common Shapes, and Transformations

Supplementary Resources

If you need more info on symmetries, these two pages are worth checking out: MathIsFun: Types of Symmetry and PurpleMath: Symmetry and Graphing.

rev. 2020-10-10