Monday, March 12, 2007

Next Lesson: The Hidden Dangers of Simplifying

(aka Holey Functions, Batman!)

Quite a few students got the hidden message, and they did it faster than I would have expected. Mostly, it went like this:

Student: "Mr. Greene, I got the answer."
(I look at student's paper and see only a string of numbers.)
Me: "What does it say?"
Student: "What do you mean 'say'? You can't read numbers!"
(I look at student meaningfully. Single or double arched eyebrow, with a slight off-center forward head-tilt. Admit it - you're doing it right now!)
(Student looks at the puzzle again.) "Oh, wait!" (Student excitedly grabs pencil and gets back to work.)

Anyway, we took a quiz at the end of the class, and they did fine, so I hope we are ready to move into simplification in tomorrow's lesson.

For the warm up, students will review finding vertical asymptotes and end behavior functions, and they will do this when given a graph only, or when given a function. (Go Representational Fluency!)

Then, I will have them analyze f(x) = (x^2-x-6)/(x+2). (Sorry, I haven't spent the time to learn LaTex yet...) They will assume there is a vertical asymptote at x = -2, and won't they be surprised when they see the graph on the TI! This will lead in to the discussion of 0/0 and holes in functions, and so forth. We'll do a couple practice problems, where students need to simplify (clearly writing the domain of the simplified form of the function) and graph (clearly indicating any holes). If there is more time left, I have a few practice problems for them to do on their own.

Wish us luck!

Robert said...

Somewhat offtopic, but Wikibooks has a good LaTeX guide here:
http://en.wikibooks.org/wiki/LaTeX