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On page 8 of the function progression document, the following statement was provided.
“Notice that a common preoccupation of high school mathematics, distinguishing functions from relations, is not in the Standards.” This leaves the impression that there should be a reduced focus on identifying relations as functions or non-functions, and yet in the same paragraph it states “The essential
question when investigating functions is: “Does each element of the
domain correspond to exactly one element in the range?” Can you elaborate on the instructional strategies used to address how functions should be identified based on these statements in the progressions document?I think I need a more precise question here. But here are some musings. If I were teaching functions I would certainly give examples where there is not a well-defined output, to emphasize the importance of that aspect of functions. For example, give a table of days and average temperatures and then ask if the temperature is a function of the day (yes) or if the day is a function of the temperature (no, because there is more than one day with a given temperature). That’s different from defining the concept of a relation and then giving students a whole bunch of relations and asking them to sort them into functions and non-functions. That can lead you into territory where the concept of “one output for each input” gets lost in a blizzard of vertical line tests (which I think most students never connect with inputs and outputs).
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