Functions: EVEN/ODD Functions and Transformations

First things first: these Sun computers are annoying, awful, awfully annoying, annoying awful, and just bloody slow.

Having gotten that out of the way, I would like to begin my blog post: Mr. Maksymchuk spent almost the entire class lecturing about functions and their transformations. First, he explained to us what a one-to-one function is:

Basically, a function cannot have an inverse if more than two elements in the domain map onto a single element in the range; if it does have an inverse, it is consequently called a one-to-one function since it must therefore have its domain mapped onto its range via a one-to-one mapping.

Mr. Maksymchuk then showed us how to employ this fact to simply determine whether a function has an inverse. We use the "horizontal line test" to do this:

Pretty self-explanatory.

Anyway, we then got to the main part of the lecture explaining what odd and even functions are:

Succinctly put, an even function has the property that f(-x)=f(x) and an odd function has f(-x)=-f(x). On a graph, even functions are symmetrical about the y-axis whereas odd functions are symmetric about the origin - i.e., an odd graph remains unchanged if you rotate it 180° about the origin.

We then applied our knowledge by doing some sample questions:





At the end, Maksymchuk talked about graphing reciprocals:




Mr. Maksymchuk then asked us to prove that 1/f(x) can never be zero. As far as I can tell, this can not be the case since we would have 0=1/f(x), 0*f(x)=1 or 0=1. What do you think?

IB