Graph of an Exponential Function
This interactive GeoGebra worksheet allows you to see what the graph of y=ax looks like for values of a from 0.05 to 5 by moving the slider. Have a go and see what happens!
You should note the following.
If a>1:
- As x increases so does y.
- y is always positive.
- As x gets large and positive, so does y.
- As x gets large and negative, y gets close to zero.
- y<1 if x<0.
- y>1 if x>0.
- y=1 if x=0.
- As a increases the graph gets steeper.
If 0<a<1:
- As x increases y decreases.
- y is always positive.
- As x gets large and positive, y gets close to zero.
- As x gets large and negative, y gets large and positive.
- y>1 if x<0.
- y<1 if x>0.
- y=1 if x=0.
- As a decreases the graph gets steeper.
If a=1, then the graph is just y=1.
If you want to return the slider to its original position, then simply click on the icon in the top right hand corner of the worksheet.