Test

I was sick on Tuesday, and that deprived me of seeing the pretest answer key. That hurt me, but what the heck -- bite the bullet. I think I didn't do too good, but not as bad as the last test. Anyway, I don't feel too choked up over it.

I used to take graphs at face value. Then I discovered a bunch of cool things. Graphs help us visualize numbers. And, with graphs, you can do cool things.

f(z) = x^2 + y^2.

http://www.math.uri.edu/~bkaskosz/flashmo/graph3d/

What does this look like? Well, it's a 3D graph. I tried to visualize it, and it was hard making a three-dimensional leap from the two dimensions, but it sets in once you realize that there are two x^2 parabolas, so, if we twist one of parabolas 90 degrees from the vertex, we create a bowl like structure in 3D:




















What does this have to do with what we do in class? This made me realize that the reason they teach us graphs is that these graphs help us visualize the answers to these equations. In the end, these are number solutions that we're looking at. This really puts things in perspective for me.