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

Overview

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.

Objectives

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

• 2.1.1 Find domain and range of advanced functions algebraically and graphically
• 2.1.2 Find the symmetries of a function graphically
• 2.1.3 Find the symmetries of a function algebraically using symmetry tests (for symmetry about the x-axis, y-axis, origin, and y=x line)
• 2.1.4 Determine if a function is even or odd both algebraically and graphically
• 2.1.5 Find regions of a function on which its graph is increasing, decreasing, or constant
• 2.1.6 Locate local (a.k.a. relative) extrema graphically
• 2.1.7 Find absolute extrema graphically and algebraically
• 2.1.8 Understand the difference between extrema points and extrema values

Terminology

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

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.