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Calculus III

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

Overview

Using the common and special graphs learned in the last lesson, we now transform them via reflections, stretches, compressions, and translations (both vertical and horizontal). Pay particular attention to how changes in the equation (changes in: coefficients, powers, and arithmetic operations) affect its graph. Look for patterns and make connections. Take advantage of the technology available to quickly graph the transformed equations and make comparisons.

Objectives

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

• 2.3.1 Recognize when a common function/graph is reflected about the x-axis, y-axis, or origin
• 2.3.2 Recognize when a common function/graph is stretched or compressed
• 2.3.3 Recognize when a common function/graph is translated vertically or horizontally

Terminology

Terms you should be able to define: reflection, stretch, compression, translation

Mini-Lectures and Examples

Supplementary Resources

If you need information about transformations, then Transformations of Graphs of Functions, Prof. Jim Michelena, Modesto Jr. College provides lots of information about all types of transformations and includes detailed examples.

rev. 2020-10-10