Graph .

I’d like to do this problem after we know about rational functions. We’ll start with integer inputs and then move to rational inputs, where we quickly run into the sort of domain problem we have with radicals and negatives.

Maybe even better: let’s play with this function again once we know about complex numbers and try to graph this function again. There’s another host of problems waiting for us there, even conceived as a real –> complex function.

[See also: http://mathforum.org/library/drmath/view/55604.html]

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