Inverse Functions #MTBoS30 Post 20

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This week we wrapped up our school year with 2 final teacher work days.  One day our department had some time to reflect onmour year.  One of our big issue is the immense amount Kentucky requires in Algebra 2.  Its nearly impossible to ‘cover’ it all, much less allow struggling math students time to process and develop a slight understanding.

I, personally, don’t worry with getting it all in.  I attempt to make the students’ time worthwhile and hopefully they leave with some deeper understanding about concepts rather than a list of procedures only 30% may be able to recall at any given time.

Anyway, we attempted to pick out 10 Big Rocks for our focus next year..the non-negotiables in a sense and that is where we will begin.  Sure we will have the “extras” ready should we achieve at a faster pace than expected.  But the goal is to truly develop reasoning and conceptual understanding of our Big Rocks.

While looking over the outline, there were a couple of things I remember thinking we needed to ensure we focused on during our functions unit.  1) composition of functions, not just in equation form, but to make sure we look at them numerically in a table of values and graphically as well. 2) a different approach to finding inverse functions.

It was Sam’s post that made me wonder if this way would make more sense for our students.
Looking at “x” think about and list order of operations.  Then, in reverse, list inverse operations and apply to x to get the inverse function.

Inverse operations and inverse order.
Is this a strategy others use as well?  A couple of colleagues seemed to really like this.
Wondering what situations it may not work…or at least reasons I shouldn’t use this approach.  Is there anything that follows this would cause issues for my students?

5 responses »

1. This is the same approach we have taken to inverse functions this year! We developed it on our own, but it looks like lots of folks are coming up with this. I really like it because it focuses on the operations, rather than simply switch and solve.

• We were past functions when I ran across Sam’s post, but I used it successfully in RTI with several students.

2. I have used this method for several years now. I love it for the regular level and low level students in Algebra 2. It makes the process very accessible to them, and seems to clarify the meaning of inverse functions. In honors, I use this strategy to introduce the concept, but we also talk about the “switch x & y” method because working backward doesn’t work on quadratics in standard form, rational functions, and exponential functions.

3. I’ve used this approach for a couple of years with my remedial Algebra 2 Ss and have had overall success with it.

4. I used this last year and found it mostly successful. I taught both this method and the switch x and y method. I think overall students preferred this method. It doesn’t work when a function has more than one variable term. A common mistake I saw in my students was trying to do it all in their heads and then making mistakes on the order of the operations. When to use parenthesis or not is also a challenge for some.