# 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.

#### Examples

• Sketch the graph of $f(x)=2x^2$. What about $f(x)=-2x^2$?

• Describe the graph of $f(x)=(1-x)^2+3$.

• The graph of $y=\sqrt[3]{x}$ 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 $g(x) = \sqrt{2x}+1$.

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 $g(x)=-2(x+3)^2-5$. Domain? Range? Vertex?