The main purpose of this activity is to understand the difference between -f(x) and f(-x). Both are reflections - but over what line?
First observe the graph given to you. Then you can change the function rule for f(x) to different parent functions. Don't change g(x) or h(x), just let them adjust on their own when you change f(x).
When you think you know the difference between f(-x) and -f(x), write it down. Then see if you can figure out why I didn't choose f(x) = x^2 as the first example.
When you get this, move on to the Dilations activity.