Here again, we will be using the parent function f(x) = and its graph.
A reflection takes whatever graph we have and flips it across either the x-axis or y-axis. The graph below has an example of each of these reflections with respect to our parent graph.
Notice that there are only two graphs. In some cases, the reflection acroff one of the axis, just gives back the original equation. To see other examples of reflections look at page 287 in your book. Here, the red graph is the equation y = -|x| and the blue graph is y = |-x|. The red is the reflection across the x-axis and the blue is the reflection across the y-axis.
The Rule for Reflections:
if y = f(x), then y = -f(x) gives a reflection across the x-axis and y = f(-x) gives a reflection across the y-axis.