If you want to have a complete graph of a function f, then these are all of the things that you should make sure show up: This should be sufficient whenever f is a twice-differentiable function whose domain is an interval, or more generally whenever f is piecewise twice-differentiable: a piecewise-defined function in which the domain of each piece is an interval and in which each piece is twice-differentiable except possibly at its endpoints. (There are weirder functions that can't be put in this form, but you shouldn't have to deal with them in this class.)
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