Transformation of functions

Topic:
Functions
In this activity, you will find out how graphs of functions are transformed by a parameter. In the applet below, is a function whose graph is red. Function , whose graph is green, will be defined as where is a positive number. Function , whose graph is blue, will be defined as where is a positive number. Your job is to explain the effects that the coefficient has on the graphs. How are the graphs of and different from the graph of ?
  1. Click the checkbox for function .
  2. Move the slider (or click on the play button at the bottom) to change the value of .
  3. What happens when ?
  4. What happens when ?
  5. Describe the effect has on the graph of the function.
  6. Uncheck the checkbox for function , Click the checkbox for function , and answer the same questions.