## Reflection: Connection to Prior Knowledge Where are the Functions Farthest Apart? - The Sequel - Section 1: Launch and Explore

While students were working on this problem in their table groups, I heard a student make a comment that really resonated with me. He said that when you take the inverse of these functions, the x-values and the y-values switch places. So subtracting the inverses gives us the vertical distance of the inverse functions which is the same as the horizontal distance of the original functions. Although it was a mouthful, I had the student say it again during the class discussion and it made sense to students.

Really, we are doing the same thing as the when we found the maximum vertical distance (subtracting the two functions) with the additional step of finding the inverse of f(x) and g(x). After students thought about it and we refreshed our memories about inverses, it definitely made sense to them. I was glad that I happened to catch this comment during the class.

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# Where are the Functions Farthest Apart? - The Sequel

Unit 1: Functioning with Functions
Lesson 7 of 11

## Big Idea: Inverses, combinations of functions, and maximization are all essential to solve a problem about horizontal distance on a graph.

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60 minutes

### Tim Marley

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