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You could start with two tables of values for x (the input variable) and y (the output value) in both. To start, each should represent a permutation on say, the set {1, 2, 3, 4, 5}, but don't use the word "permutation." Label one "Table A", the other "Table B". For each line in Table A, introduce the notation A(1)=, A(2)=, etc. Similarly, for Table B. ...


Many answers already, so I'll keep this one short: it has been realized by researchers in didactic that one difficulty in the concept of function is that it changes status: at first each function is considered as a process (a verb in @ΦDev's answer); they meet several of them, each being akin to a (unitary) operation, not very different from addition or ...

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