The purpose of this whiteboarding activity was to look at zeros of rational functions - from the numerator - and significance of double, triple etc. roots. We also examined vertical asymptotes of rational functions - from the denominator - and significance of order two, three etc. of the factors in the denominator. Lastly we examined when the horizontal asymptote was y = 0 (degree of numerator < degree of denominator) or when the horizontal asymptote was y = some other number other than zero (degree of numerator = degree of denominator) so horizontal asymptote ended up being y = (Leading coefficient of Numerator / Leading coefficient of the Denominator).

Here are some photos from the whiteboards as we worked our way through this.

We started with something that would have lots of confusion - included a hole

And then we went through this progression.

Some of my work so students could make some generalizations.

Students now a days!

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