Comments on: Function Transformations

By: samjshah

samjshah — Sat, 02 May 2009 11:50:06 +0000

@Jonathan: I put the book on my amazon wishlist, so I’ll remember to buy it for myself.
@Travis/Jonathan: That’s great to highlight the symmetry involved with x/y transformations. I wish I did that this year. I taught the reason behind it a bit differently, so it didn’t really stick with them. Next year…

Thanks for your comments.

By: jd2718

jd2718 — Fri, 01 May 2009 22:47:04 +0000

y – k = fn(x-h)

where (h,k) is the shift. Ugly, I know.

Jonathan

By: Travis

Travis — Fri, 01 May 2009 13:53:52 +0000

One of my personal irriations with the “transformations of functions” approach is the seemingly opposite affects algebraic operations have when applied only to the “x” variable versus the function itself (for example, +2 appended to f(x) shifts the graph UP, whereas +2 appended to the x alone shifts the graph right. I instead like to teach how the transformations affect the graphs of ANY equations, and then treat the graphs of functions as a special case. For example, in the graph of any equation involving x and y, replacing a variable v by v-a shifts the graph a units in the direction of the v axis — and this is true whether v is x or y. This not only helps explain where the function transformations come from, but also why the equations of various conics are, well, what they are!

By: jd2718

jd2718 — Sun, 26 Apr 2009 15:31:52 +0000

Do you have the Gelfand book: Functions and Graphs? Less than 10 bucks. I recommend it, and it might suggest ways to tweak your stuff... Jonathan