It seems that one of the most confusing topics in high school mathematics is transformation of functions. This file shows a demonstration to the students, which hopefully communicates visually what happens to the graph when we modify the function itself.
During the Activity
Teachers should use the TI-Nspire Computer Software (in normal view) to demonstrate to the students what happens to the graph of f(x), when it is modified to model a*f(x+h)+k.
The first problem uses sliders for a, h, and k to demonstrate to the students that it does not matter what the function is...a, h, and k all do the same thing. Problem 1 uses the graphs of y=x^2, y=abs(x), and y=sqrt(x) to provide this demonstration.
Problems 2 & 3 each use a piecewise function to model that the function itself is not important, the graph moves in the same manner regardless of whether or not a student can recognize the function being graphed. The List & Spreadsheet pages for Problems 2 & 3 are only there to provide the data for the scatter plots...they should not be changed.
After the Activity
Teachers can also give the students verbal/written directions along the lines of "graph a quadratic function that has been shifted down 4 units and to the left 5 units," mixing up the line of questioning to assess many different types of functions.
Teachers can use either Screen Capture and/or the Make Presenter options of the TI-Nspire Navigator to quickly assess student understanding.