I printed this out and cut apart the functions.

Function Composition Relay

Each person in a group got a different function. Then I wrote on the board the definitions of composition (f (g(x)) and g(f(x))) and explained that it was like a relay, with the inside handing off to the outside. I started with an example of composition on a number: f(g(2)) and explained that this meant that g would take the 2 and do "its thing" to the 2, then hand off the result to f and then f would do "its thing" and get the final result. I posted several more examples of composition on a number on the board, one at a time, and had them calculate the results in their group. We even did composition of three and even four functions. Then I asked them "What if I want to know a

*formula*for the relay so that I don't have to actually

*do*the relay in order to figure out how it turns out? In other words, what if I want to find the composition

**on x**?" We then did f(g(x)) together. They were able to do any combination of function composition I put on the board, including (with a little help) the f(g(h(j(x)) composition. It went great! I will definitely be teaching composition as a relay from now on.

I will say that my students

*still*struggled to recognize the symbol for composition when it showed up on the test. If I reminded them that it was the "relay" operation, they would go "oh, yeah!", so I'm going to have to give them some more independent practice with the notation next year....

Do you have a file or picture? All I can see is an empty white box? :(

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