In a parabolic curve it would be called an asymptote, where only one integer is exluded. If multiple integers are excluded, or you are dealing with piece-wise functions it is called a jump discontinuity.
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i think its called a break. :]
It depends on what variable is represented by the graph.
its actually called "a break".
Yes.
What do you mean by "top of the graph"? Do you mean the highest value? The top of the graph is called "the top of the graph" There's no term for it.