Teaching horizontal asymptotes of rational functions can be tricky without resorting to “tricks”, while still building some “function-sense”. This year I gave them a function and they plugged in larger and larger values (positive and negative) to essentially find the limit as x->infinity. Some nice previewing of a skill that we’ll address later on in 4th quarter. Then they use a bunch of examples that we gave to try and figure out the “pattern”. I break their rule a couple of times and after reforming their rules, they came up with this (student created, not teacher):
Here’s a subset of the stuff on the board that they were given in order to find their rule:
Interesting work by a student to explain the second and third cases. They added in the “0x^2” so that it fit their rule. Love it!