Lesson Objectives
• Learn how to reflect a graph across the x-axis
• Learn how to reflect a graph across the y-axis

## How to Reflect a Graph Across an Axis

Another type of graphing transformation is a reflection. When we talk about a reflection, it can be thought of as a folding or flipping of the graph over the line of reflection. $$g(x)=-f(x)$$ g(x) is the graph of f(x) reflected across the x-axis. $$g(x)=f(-x)$$ g(x) is the graph of f(x) reflected across the y-axis. Let's look at an example.
Example #1: Describe the transformation from f(x) to g(x). $$f(x)=|x|$$ $$g(x)=-|x|$$ Since g(x) = -f(x), we can state that g(x) is the graph of f(x) reflected across the x-axis.

#### Skills Check:

Example #1

Describe the transformation from f(x) to g(x). $$f(x)=\sqrt{x}$$ $$g(x)=\sqrt{-x}$$

A
Reflected across the y-axis
B
Reflected across the x-axis

Example #2

Describe the transformation from f(x) to g(x). $$f(x)=x^2$$ $$g(x)=-x^2$$

A
Reflected across the y-axis
B
Reflected across the x-axis

Example #3

Describe the transformation from f(x) to g(x). $$f(x)=x^4$$ $$g(x)=-x^4$$

A
Reflected across the y-axis
B
Reflected across the x-axis         