Section 2.6 - Transformations: Compressions, stretches, and reflections

Section Objectives

Transform a graph by reflecting about an axis.

Transform a graph by compressing or stretching.

Carry out a sequence of transformations on a graph.

Transformations

We have already discussed translations (shifts) of graphs. This table summarizes the transformations we're seen, as well as a few new ones.

Transformed Function

Effect on Graph

Graph of shifted units up

Graph of shifted units left

Graph of reflected about -axis

Graph of reflected about -axis

Graph of stretched vertically

Graph of compressed vertically

Graph of compressed horizontally

Graph of stretched horizontally

Examples

Sketch the graph of . What about ?

Describe the graph of .

The graph of is vertically stretched by a factor of 5, then it is shifted 3 units right and 2 units down. What is an equation for the new graph?

Sketch the graph of .

Important idea: When a function is transformed, its special features, such as domain, range, and intervals on which it is increasing/decreasing, change in corresponding ways.

Discuss the features of the function . Domain? Range? Vertex?