I’m teaching my Algebra 2 students about transformations. We look at how f(x) changes when you write f(x) + 5, or 2*f(x), or -f(x), etc. Things get a little bit dicier when we start playing with the x-values, though, as opposed to the y-values.

If g(x) = f(x-3), what does the graph of g(x) look like? How do you teach this to your students? I got my inspiration from Will Rose on this one: check it out.

f(x) is a function monster, and it can only *eat* numbers between -2 and 4.

Now we define g(x) = f(x-3). We know that f eats numbers from -2 to 4. What numbers can g eat?

So how do you teach a) horizontal translations, b) horizontal dilations, and c) horizontal reflections to your students? Go ahead and share your great ideas in the comments.

### Like this:

Like Loading...

*Related*

[…] Key uses a function monster to illustrate […]

When I teach transformations to students in Algebra 2, I discuss how functions are written in terms of the y-value. So stretching/compressing, reflecting, and translating vertically (which changes all y-values) can be applied directly to a function in terms of y. The difficulty comes with horizontal movements. So I have students re-write functions in terms of the x-value, apply the transformation, and re-write in terms of y. At this point i’d ask them to examine what changed from the original to now.

Also with translations, we discuss a function such as y = 3x + 1. I show them that when we move this function up on the y-axis, it simultaneously moves to the left on the x-axis (counter intuitive) and when we move it down on the y-axis, it simultaneously moves right on the x-axis. We then discuss the slope of the function which states for every 3 units the function moves vertically, it will move 1 unit horizontally. So to move 2 units left, we must move the function 6 units up. 3x + 1 + 6.

I have struggled with this in the past, and this year decided I’ll teach the concept using encryption. Hopefully the encryption context will not just be fun but will also make the idea easier to understand. Briefly, the idea is to consider the code

1 –> A

2 –> B

etc.

Let’s call this code f(x). So to encode “Hi”, you’d transmit the message “8-9”. But what if you decide to use the code f(x – 3). Adding a predetermined shift would let you keep your code more secure. Using f(x – 3), the message for “Hi” is “11-12″…see how it shifted to the right by 3?

I wrote up this idea here:

http://ijkijkevin.wordpress.com/2013/09/06/how-i-want-to-teach-horizontal-function-transformations/

Dan was a little skeptical, but Kate thought it could be really cool. Curious what you all think. In my opinion, the advantage of this approach is that you can have students encode their own messages to each other and ask them to check their work by decoding before exchanging papers. Students who shift to the left 3 will catch their own mistake when they decode their message, so the “aha” realization will come from themselves rather than from my explanation.

The approach can also be extended to the concepts of period and phase shift for sinusoidal functions.

I love your function monster idea and will be using it in my classroom! I don’t have any crafty ways to teach these topics to my students so I look forward to others’ ideas!