Exponential Transformation
Transforming Exponential Graphs
Below is a graph of which is a green curve and which is a blue curve, which may be on top of the green curve if and .
We are going to change the values of and and consider the changes to the shape and position of the curve.
Changing the value of b
Increase the value of . What happens to the curve?
Decrease the value of . What happens to the curve?
Tick the "Show Asymptote" check box. The asymptote should be shown as a dashed orange line.
How does the equation of the asymptote change as the value of changes. (remember that horizontal lines have the form .
Changing the value of a
Return to zero. With the blue curve should overlap the green curve.
Select the "Show Intercept" check box.
Change to . What is the intercept now? How far above the asymptote is the intercept?
Change to . What is the intercept now? How far above the asymptote is the intercept?
Do the same with and . What do you notice?
Negative values of a.
What happens when ? How does the position of the intercept compare to the asymptote?
Try changing to , , , and . Do you see the same thing with regard to the asymptote and the intercept?
Changing a and b
With , change to .
Try to predict what is going to happen when you now change . Do you expect to see the same relationship between the position of the asymptote and the position of the intercept that we saw before?
Change the value of . Do you see what you predicted?
Try various values of and . Do you see what you expect.