Of all the topics on the math section, my students seem to have the most trouble with functions. Did your heart rate increase when you read the word “function”? Okay – maybe not. But a lot of students get frazzled by function questions, so here’s some help:
Let’s start with the psychology. I like to ask my students “what was the first grade in which you ever leaned a math function”? Their answers typically run from 7th to 11th grade. Wrong! You learned your first function in 1st grade. Addition and subtraction are functions, as are many other concepts you learned throughout grade school.
A mathematical function is simply a set of instructions that tells you what to do with one or more values. Addition is actually a hard one, since you have to memorize all of those combinations (you’re not born knowing what 8 + 3 is).
First grade teachers like to make things simple. They just show you a chart that says something like 8 + 0 = 8, 8 + 1 = 9, 8 + 2 = 10, etc. But high school teachers can’t make things that simple, because they know you’d laugh at them. So they show you something like
f(x,y) = x + y
…and say “here’s an easy one.” Who’s laughing now?
But wait…the only thing that’s new there is f( ). Your teacher tells you that f( ) means “eff of.” But I don’t know what “eff of” means either. So I say that it means “start with.”
So f(x,y) = x + y means “start with x and y, and end up with their sum.”
And f(3,4) means “start with 3 and 4, and end up with their sum,” which is obviously 7.
Let’s look at one more:
f(x) = 2x + 4 means “start with x, and end up with twice x plus 4.”
f( ) looks scarier than + or √, because it looks like 3 symbols. Just think of it as one symbol.
Okay, that was pretty elementary stuff. But my point is that overcoming “function fear” is the first step toward mastering function problems. More tips on functions will follow shortly.