Friday, October 9, 2009

A discussion of asymptotes

One of the objectives in the Intermediate Algebra class is identifying some basic properties of a relation from looking at a graph (domain, range, is it a function). So, on a test I put in a graph that could roughtly correspond to -log (-x). This graph has the y-axis as an asymptote.

While I have done this a few times before, this is the first time I've had members of the class question whether it was possible for a graph to be an asymptote. As one student said, "Doesn't it need to either go straight up or curl back?" No, not exactly.

So, to make it easier to understand, I talk about how y=1/x behaves as x increases. I won't bore with the details. I get to end the discussion with one of my favorites things to tell a student: It makes perfect sense, it's just counter-intuitive.

If you know anything at all about mathematics, you should know that.

1 comment:

J said...

I think infinity (and the infinity sign) should be nixed, at least until calculus+. Maybe permanently. It just makes naive students swoon.