### Blah blah asymptote blah blah intercept

Three of my four classes are full of students who seem to be getting at least something out of my efforts, but lately I can’t think about my early afternoon precalculus class without being reminded of this Far Side cartoon:

For whatever reason, the students who can’t solve linear equations, the students who can’t add fractions, and the students who can’t even come close to formulating an equation from a word problem, all ended up in this section. A typical Q&A session in that class goes something like this:

Student: (after I’ve graphed one function on the board) So basically, when you’re graphing a function, it goes positive-negative-positive-negative, and has two vertical asymptotes.

Me: (not knowing where to begin) Well, no, not really: in the case of the example on the board, yes, but that’s because of the factors of the two polynomials in the quotient. (expands on this a bit, explaining where the zeroes and intercepts came from, again) You need to look at the factors of the numerator and denominator, and take test points in all of the intervals that you obtain from the critical points. (does example on blackboard) Does that make sense?

Student: So basically what you’re saying is, yes, in general there’s two vertical asymptotes and the graph goes positive-negative-positive-negative.

Most of these students would benefit from a good, solid, *grade nine* math class, and I’m at a loss over what to do with a university precalculus class full of them.