Function concepts -- introduction

The unit on functions is the most important in the Algebra II course, because it provides a crucial transition point. Roughly speaking…

• Before Algebra I, math is about numbers .
• Starting in Algebra I, and continuing into Algebra II, math is about variables .
• Beginning with Algebra II, and continuing into Calculus, math is about functions .

Each step builds on the previous step. Each step expands the ability of mathematics to model behavior and solve problems. And, perhaps most crucially, each step can be frightening to a student. It can be very intimidating for a beginning Algebra student to see an entire page of mathematics that is covered with letters, with almost no numbers to be found!

Unfortunately, many students end up with a very vague idea of what variables are (“That’s when you use letters in math”) and an even more vague understanding of functions (“Those things that look like $f\left(x\right)$ or something”). If you leave yourself with this kind of vague understanding of the core concepts, the lessons will make less and less sense as you go on: you will be left with the feeling that “I just can’t do this stuff” without realizing that the problem was all the way back in the idea of a variable or function.

The good news is, variables and functions both have very specific meanings that are not difficult to understand.