Fun With Functions

There looks to be a high likelihood that I'll have either one or two Grade 11 Math students to tutor by the time September rolls around, which is a big departure from what I've been doing up to now. My current student body is composed of Grade 5s through Grade 8s, and the curriculum demands for that range are well within my ability to teach, pretty much from memory.

High school Math particulars, on the other hand, are not always readily available to me off the top of my head all these years after I graduated. For example, before I spent time helping Tammy bring up her Grade 9 mark (about 9 years ago now), I'd forgotten that y = mx + b was one of the two standard forms for defining a line (with Ax + By + C = 0 being the other) and I certainly didn't recall what "SOHCAHTOA" stood for ("Sine = Opposite side over Hypotenuse, Cosine = Adjacent side over Hypotenuse, and Tangent = Opposite side over Adjacent) nor how (or even when) to complete a square, in Algebra. By the time Tammy finished Grade 9, though, I was pretty solid on those delightful topics and a whole lot more. Then she did Grade 10 largely on her own (with a fantastic mark to show for her efforts) and I can't recall helping her at all for Grades 11 or 12. Thus, my knowledge of Grade 11 Math, as of few days ago, was about 30 years old.

Looking at the Ontario curriculum, I discovered that Grade 11 Math is Functions. That was probably true even when I went to high school, but I honestly don't remember what subjects were in which years. Anyway, I quickly realized that I don't remember a whole lot about Functions, and therefore it was time for me to go back to school!

Well, figuratively, anyway. I've spent several hours over the past two days reviewing Functions lessons and problems on the Internet, and am already starting to feel more confident about it. I got a big boost in that department just before lunch today, when I was reading up on how to determine the range of a function. I'd found a very nice website that had some Flash applications covering several of the key basic attributes of a function. When I got to the end of their explanation for how to determine a function's range, though, it didn't look to me like their example was right. So I used the technique that they'd described, but did the algebra myself... and discovered where they'd made their mistake! Using my answer, the values actually worked when plugged back into the original question. That was the moment when I knew that I actually got the material, and that I really was just re-discovering it, rather than having to learn it all over again from scratch.

I'm having a great time doing this, as, really... what's more fun than Math?? (Correct answer: not much!)