# Functions

### Intro

In this unit, we will be doing two main things: learning what functions are, and learning how to draw graphs. There will be plenty of plotting...but not much scheming. Sorry.

In order to precisely define a function, we'll do a bit of set theory first, which is something you usually don't get to until college or maybe even graduate school. However, we can tell that your brain is about to blossom like a brilliant orchid, and we don't want to see that kind of growth be stunted. Besides, once it's finished fully blossoming, we can then pick your brain.

We will also learn what *relations* are, in a sense that has nothing to do with your aunts and uncles. You won't be running into any of these at your family reunion, unless some of your relatives are real algebra-hounds.

We'll draw lots and lots of graphs, also known as "pretty pictures that can make your life easier." Be careful, however, since this can also refer to the diagrams included in the instructions on how to assemble a desk from Ikea.

We'll see how to go from equations to graphs and from graphs back to equations. That's right, we're going to buy you a round-trip ticket. We'll spend a while looking at linear equations, which are equations that produce graphs of straight lines. (See the word "line" in the word "linear?")

Finally, we'll look at some types of equations that *aren't* linear and see what kind of pictures we get out of those. We're hoping hearts and rainbows, but we're not counting our chickens.