Feeling Rational

I was observed today. Observation 3/4… What does that mean? The semester is almost over and I’m almost ready to enter the world of professional working.

Anyway, today in class we were introduced to Rational Functions.  My observer recommended using the following activity as a subsequent practice problem so I thought it might be nice to see! Have some fun with it!

Graph xover2 and 2overx









What do we observe about the graphs of these equations?

How do they behave?

Why do you think this is?

It is actually quite beautiful to observe how the slight change in position of x causes such a stark change in the graphs.  This is the type of relationship that causes great discussions in the classroom, and leads to great conclusions and conceptual understanding in students. This is a rational development for proposing new information to students, and this is what makes learning fun.