In the sketch below you will be able to see how the sliders h and k effect several different functions. By the end of the activity, students should be able to determine the effect of both sliders on the general function

external image gif.latex?f(x)=(x-h)+k

Students will also be able to graph functions of the general form above, but that will come later in the activity. It is important for students to have some general idea of how to graph functions using a table and or graphing calculator. As a warmup I hade students graph a linear equation and a quadratic, both showing a vertical shift using a table of values. I also demonstrated how to use "key points" and move points in a general direction. I hope you enjoy this activity. Special thanks to Linda for some nice updates. Here is the Actviity

Function Shifts

Use input boxes or select the "show sliders" box to to change the values of h and k and show their effect of f(x)

Use the sketch to show how the parameters h and k effect several different functions.

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

Nicholas F. Bennett, September 6, 2011, Created with GeoGebra