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