Lesson Plan: Function Transformations: Dilation Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to identify function transformations involving horizontal and vertical stretches or compressions.
Objectives
Students will be able to
- understand horizontal dilations of the function :
- corresponds to a horizontal dilation of scale factor ,
- when , the result is considered a stretch,
- when , the result is considered a compression,
- understand vertical dilations of the function :
- corresponds to a vertical dilation of scale factor ,
- when , the result is considered a stretch,
- when , the result is considered a compression,
- identify the resulting graph of a given graph when dilated horizontally or vertically,
- sketch the graph of a given basic function when dilated horizontally or vertically,
- understand how to combine a horizontal and a vertical dilation algebraically,
- identify the rule of a function for which a horizontal or a vertical dilation is represented graphically,
- understand that certain horizontal dilations may be equivalent to vertical dilations depending on the symmetry of the given function.
Prerequisites
Students should already be familiar with
- function notation,
- basic function graphs, including simple linear, quadratic, cubic, radical, and reciprocal graphs.
Exclusions
Students will not cover
- function transformations involving translation and reflection.
