In this activity you will use a slider to change the basic (parent) functions. You will be able to change value of the sliders ao, ai, h, and k to transform the function by moving these sliders.
GeoGebraTube Worksheet on Function Transformations

You can move the lightly colored panel as needed to see what is below it.

What effect does changing the parameters of an equation have on its graph? In this activity, you will explore the effects of changing the parameters one at a time.

g(x) = ao f(ai x – h) + k
Fill in tables on the following pages using the GeoGebra **Transformations of Families of Functions** document above and make observations using the guidelines below.
  • · Click the ao slider on each page to manipulate the variable ao. Note what ao does to the graphs of the functions.
  • · Click the ai slider on each page to manipulate the variable ai. Note what aidoes to the graphs of the functions.
    • Caution: ao and ai can mirror the results of each other when they are to only changes to the function. Each as a unique function, these functions are very different, yet they can mimic each other.
  • · Click the h slider on each page to manipulate the variable h. Note what h does to the graphs of the functions.
  • · Click the k slider on each page to manipulate the variable k. Note what k does to the graphs of the functions.

Prior to filling out the columns in the table on the actions of the sliders, be sure to examine the effects of ao and ai before and after you have changed the values of h and k separately. Without changing these value ao and ai will mimic each other, especially with the linear function.
Example actions for all functions prior to recording in the tables on page 2:
  1. Move ao to 2, observe action and return to original setting of 1.
  2. Move ai to 2, observe action and return to original setting of 1.
  3. Move h to 2, observe the action.
  4. Move ao to 2, observe action and return to original setting of 1.
  5. Move ai to 2, observe action and return to original setting of 1.
  6. Return h to original setting of 0.
  7. Move k to 2, observe the action.
  8. Move ao to 2, observe action and return to original setting of 1.
  9. Move ai to 2, observe action and return to original setting of 1.
  10. Return k to original setting of 0.