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UCD Maths Support Centre

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.