Transformations+of+Basic+Family+Functions

In this activity you will use a slider to change the basic (parent) functions. You will be able to change value of the sliders **a** o, **a** i , **h**, and **k** to transform the function by moving these sliders. You can move the lightly colored panel as needed to see what is below it.
 * GeoGebraTube Worksheet on Function Transformations ||
 * media type="custom" key="27634694" ||

**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) = a o f(a i 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 **a** o slider on each page to manipulate the variable **a** o . Note what **a** o does to the graphs of the functions.
 * · Click the **a** i slider on each page to manipulate the variable **ai**. Note what **ai**does to the graphs of the functions.
 * Caution: **a** o and **a** i 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 **a** o to 2, observe action and return to original setting of 1.
 * 2) Move **a** i to 2, observe action and return to original setting of 1.
 * 3) Move **h** to 2, observe the action.
 * 4) Move **a** o to 2, observe action and return to original setting of 1.
 * 5) Move **a** i 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 **a** o to 2, observe action and return to original setting of 1.
 * 9) Move **a** i to 2, observe action and return to original setting of 1.
 * 10) Return **k** to original setting of 0.