## Graph of an Exponential Function

This interactive GeoGebra worksheet allows you to see what the graph of y=a^{x} 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.

## Contact the Maths Support Centre

James Joyce Library, University College Dublin, Belfield, Dublin 4, Ireland. T: +353 1 716 7536 | E: msc@ucd.ieIf you enter the library the MSC is the glass room with the orange and green circles just to the left opposite the entrance. You will need your valid student card to gain access to the James Joyce Library.