Section 2.6 - Transformations: Compressions, stretches, and reflections

Section Objectives

  1. Transform a graph by reflecting about an axis.
  2. Transform a graph by compressing or stretching.
  3. 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 FunctionEffect 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













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.