Classically in mathematics we talk about functions using language like f(x) and f o g (x) or "as long as the domain of the fuction remains consistant with the real numbers, then the range will occupy the same solution set as the subdomain." If you want your head to spin, do a google search for "calculus functions" and go down a few hits.
But as we showed in class today there are easier ways to think about this. I'd like to toss out another one here:
A function is just a way of pairing things from one group to things from another group. There are two catches:
Catch one: Every item in the first group has to be used.
Catch two: Every item in the first group can only have one thing in the second group paired with it.
Here's an anlogy to help frame this as you talk to your student:
Say you have a cupboard that is full of Tupperware (or something similar). It's been a long time since you organized it, so it's all piles of bowls, boxes and random lids. So you set out to clean it. You put all the bowls and boxes into one pile (our Domain), and you put all the lids in the other pile (our Range).
Now the important thing is to be sure that every bowl you have has a lid. That hits rule 1. So you pick up a bowl, find a matching lid, and set it asside. The other thing is that even if you find two lids that fit the same bowl, there's no real need to keep both lids. You have a bowl. You have a lid. You're good. Drive on, private.
In other words, every bowl gets exactly one lid, every bowl gets used, and you use the rule of "bowl and lid have to fit together" to pair them. The rule becomes known as a Function.