# Function Transformations

I just wanted a quick post to share the documents I created to teach function transformations. All documents are in .doc format. They aren’t flashy, but they really got students thinking about everything. (This is a regular Algebra II class.) They nailed the final assessment, and are now doing amazingly on transformations of exponential functions. In other words, I see my work as a success.

Function Transformations 1 BASIC INTRODUCTION (here): HW (here)
Function Transformations 2 UP! DOWN! LEFT! RIGHT! (here): HW1 (here) , HW2 (here & here)
Function Transformations 3 VERTICAL STRETCHING (here): HW (here)/ Solutions (here)
Function Transformations 3.5 PRACTICING THINGS STEP BY STEP (here)
Function Transformations 4 HORIZONTAL STRETCHING (here): HW (here) / Solution (here)

Also I handed this practice sheet out to all students to practice their 8 base functions (here).

Just so you know, I don’t always teach via handouts. But with all this graphing, I decided it made good sense.
I’m happy if you want to critique them, or make suggestions on how to improve them.

1. 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

1. 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!

2. y – k = fn(x-h)

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

Jonathan

3. samjshah says:

@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…