What does the graph of a rational function look like?

READ instructions bottom and INTERACT with the GeoGebra applet below.
Click on the icon to reset the diagram.

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Investigation Steps

  1. Move the red point A on the slider. How does the graph change?
  2. Reset the diagram. Move the blue point B on the slider. How does the graph change?
  3. Reset the diagram. Move both slider points. Observe the graphed function. How does it change?
  4. Can you explain why there are sometimes three parts of the graph and other times only two?

January 2006, Steven Lapinski. Applet created with GeoGebra.