The final topic in our unit 1 - Inverse Functions. Again, this is covered in Algebra 2 but we take it that little bit step up.
We start with some "big ideas" behind inverse functions.... It's inverting the original function by "switching the x & y", the graph is a reflection over the line y = x, the domain of the inverse equals the range of the original.
It's the later statement that becomes more of a focus. Because there can be some domain restrictions that result from the original function. I always like to start with a square root function and find its inverse. We really break this down by identifying the domain & range of the original and examining the graph. (I have students find the domain without the graph and then verify and find the range using the graph - we use TI graphing calculators).
Of course students now want to generalize that you just switch the domain & range when describing the domain & range of an inverse. So I have to work through an example that starts with a quadratic. They see that the range of the inverse is not the same as the domain of the original.
And we also get into some funky algebra. That is finding the inverse of a rational function. Something they saw but probably didn't master in Algebra 2. Good algebra skills to develop. Especially since we'll be using them in verifying identities in trig later in the year.
Yes of course, I have an ISN insert for Inverse functions.
And here is my "right hand reflect examples" for my ISN.
One thing I need to incorporate in is some more inverse application problems. Ran into a blip this year as I got quite sick so this lesson was covered by a substitute teacher via my powerpoint notes. So it wasn't as good as I would like it and I left out application work. There's always next year!
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