Composing Transformations

Enter a function f(x) in the input box at the top center of the screen. Explore the effect of the two Translation transformations Th and Tv as well as the effect of the two Dilation transformations Dh and Dv Now imagine composing a translation with a dilation. The possibilities are ThDh or DhTh ThDv or DvTh TvDh or DhTv TvDv or DvTv When does the order of the transformation matter? When not? Why? What other questions could/would you pose to your students based on this applet?