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@daniela8128 @stuartmacalpine @tedcowan7 2/2 so that means for all x values on f( x+2) they grab the heights of the x values 2 to the right on the old function . That means the whole of the old function moves 2 units to the left . With this foundation and articulation , other transformation might prove easier to explain
@daniela8128 @stuartmacalpine @tedcowan7 1/2 Nice idea. For the activity I don’t want just pattern spotting , I want students to “see” why the whole graph moves to the left for f ( x + 2) . Teacher nudging is key here. “ oh, see when you feed 3 into the new function it maps to the same height as 5 in the old function
@daniela8128 @stuartmacalpine @tedcowan7 2/2, but we do lose the functional notation when tackling relations defined implicitly, so I suppose it just depends on what we want as the conceptual understanding
@daniela8128 @stuartmacalpine @tedcowan7 1/2 Agreed @daniela8128
I suppose the usual introduction of functions and relations defined explicitly leads to this type of approach. It would be interesting to design an activity for, say, horizontal AND vertical translations of a circle.then deeper thinking needed.