# Functions

### Topics

We know how to use a number line to visualize where numbers are. For example, to visualize the numbers 0, 5, and 6 we could draw this:

This number line is **horizontal**, which means that it is oriented in the same direction as the horizon. A horizon is that thing that swallows up the sun every evening. Don't go anywhere near it if it hasn't been fed.

To draw a graph, we start with a horizontal number line labelled *x*, on which 0 is marked.

Next we add a vertical number line whose 0 matches up with the one on the horizontal number line. The word "vertical'' comes from the word "vertex, '' which, among other things, means "The point in the heavens directly above a given place." That's according to the Oxford English Dictionary, and those guys know their stuff.

This definition makes sense if we think about going to the "point in the heavens'' directly above 0 and drawing a line straight downward from there. We won't talk about where that line would go straight down *to* in this scenario; we'll just call it "the bad place." The Oxford English Dictionary had nothing to do with this one.

Now we label the vertical line *y*.

The lines we've drawn are called **axes**. Not axes, like the kind you use to chop wood. Those are far too dangerous for the world of algebra. Instead, it is pronounced "ax-ees, " where you stress the second syllable. Go ahead, try it. Again, even louder. Still louder. You just woke your mom up, didn't you? Hey, you walked right into that one.

The horizontal line is the ** x-axis** and the vertical line is the

**. To remember which one is which, we know that**

*y*-axis*x*comes before

*y*in the alphabet, so the

*x*-axis is the line we drew first (the horizontal number line) and the

*y*-axis is the line we drew second (the vertical line). Or you can think about it this way: a "xylophone" is a horizontal musical instrument, while the string of a "yo-yo" goes up and down. We have like a hundred of these. We could go on all day.

The place where the axes cross is called the **origin**. This place corresponds to 0 on both number lines. "Origin" starts with "O, " which looks something like a "0." We're only going to give you one helpful way to remember this one. We're feeling stingy.