NOTE The (graph) tag is dead. Long live the graph...ing-functions tag. See here.
At the moment, there is a discussion about the tag graph; the suggestion is to replace it with a better name, so that the questions from graph-theory are not tagged by this tag.
In the comments we came also to the questions what should be the content of this tag (or its replacement). The tag-excerpt at the moment says:
Questions regarding graphs of functions. Questions about graphs with vertices and edges should use the (graph-theory) tag instead.
This sounds (at least to me) as if this tag could be used for any question where the notion of the graph of the function is relevant. However in some of the comments it was suggested, that this tag is only for questions about plotting graphs of functions and the "basic stuff" concerning graphs. (I am not able to define more precisely what I mean by basic stuff, let us just say that this includes only things not trespassing into more advanced teritory, such as real analysis, general topology, functional analysis.) Probably many MSE users use this tag only in this sense.
But there are also questions tagged graph, where this tag is used in broader sense, such as:
I think it would be good if we could agree on the meaning of the tag and edit the tag-excerpt/tag-wiki accordingly, so that they can serve as a guide when tagging a question.
EDIT: The tag graph has been blacklisted and the questions have been moved to a new tag named graphing-functions. The new name for the tag is definitely not for questions about graphs of functions in general (as in the examples given above). So I consider this discussion resolved and I have accepted the more special answer.