Rational Functions - Looking at Zeros, Vertical Asymptotes and Horizontal Asymptotes

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

 

Reciprocal Functions

The task today was to look at a function f(x) and its reciprocal 1/f(x). We were looking for connections between the two.

The first thing I asked groups (visible random) to do was graph y = x and the reciprocal y = 1/x. When they were done I had them graph y = x^2 and the reciprocal y = 1/x^2.

Here is what it looks like.