Composing Transformations

Enter a function [i][b]f(x)[/b][/i] in the input box at the top center of the screen.[br][br]Explore the effect of the two Translation transformations [i][b]T[/b][/i][sub][i][b]h[/b][/i] [/sub]and [i][b]T[sub]v[/sub][/b][/i][br]as well as the effect of the two Dilation transformations [i][b]D[sub]h[/sub][/b][/i] and [i][b]D[sub]v[/sub][/b][/i][br][br]Now imagine composing a translation with a dilation.[br]The possibilities are[br][br][i][b]T[sub]h[/sub]D[sub]h[/sub] [/b][/i]or [i][b]D[sub]h[/sub]T[sub]h[/sub][br]T[sub]h[/sub]D[sub]v[/sub] [/b][/i]or[i][b] D[sub]v[/sub]T[sub]h[/sub][br]T[sub]v[/sub]D[sub]h[/sub] [/b][/i]or[i][b] D[sub]h[/sub]T[sub]v[/sub][br]T[sub]v[/sub]D[sub]v[/sub] [/b][/i]or[i][b] D[sub]v[/sub]T[sub]v[/sub][/b][/i][br][br]When does the order of the transformation matter? When not?[br]Why?[br][br][color=#ff0000][b][i]What other questions could/would you pose to your students based on this applet?[/i][/b][/color]

Information: Composing Transformations