How to “Break” Your Graphing Calculator

A conversation with a colleague on function operations reminded me of one of my favorite “Oh Wow!” moments from math class.

You’ll need a TI-83 or 84.  This is a case where the Nspires are too nice for our use.

Enter functions as shown below.  We are interested in the rational function which comes from dividing the two previous functions:


Since the denominator is a factor of the numerator, we can simplify the expression, resulting in a linear function when we graph.  But what about x=-3?  What happens there?  Let’s explore a bit:

Screen 2

Zoom in even more….doesn’t seem all that interesting…..


Pretty boring.  But tell your students to keep zooming.  And then….

….wait for it……


Screen 5

Zoom in even more….

Screen 6

This is a nice reminder that, while we may simplify a function, we are still looking at a quotient and need to consider the parent functions used in the division.  And the “noise” we get here is a result of the algorithms TI calculators utilize to plot the points.  Actually, if somebody has a better explanation for the noise, I’d love to hear it.  Some “new” calculators will now show the hole in this function, like my new man-crush, the Desmos calculator:


But the noise is more fun.

4 responses to “How to “Break” Your Graphing Calculator

  1. Thanks for the love! The man crush is mutual and it’s always exciting to be included in your posts. Happy graphing!

  2. Pingback: #Singulariteiten: gekke, dwarse punten in #grafieken |

  3. Thanks for sharing,find here modern calculator @

  4. Cool stuff.

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