Do functions having two separated curves (or more) like that one when plotted (that's a special elliptic function) have a special name?
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2026-04-01 19:08:52.1775070532
Vocabulary about shape of some functions
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I’m not sure what you’re referring to as “functions” here. To decompose this graph into the graphs of two functions, you’d have to split it along the $x$ axis, but that doesn’t seem to be what you have in mind. I suspect that you don’t actually mean functions in the usual sense of the term, but graphs of relations. In your example, the graph you show is the graph of the relation $y R x\Leftrightarrow y^2=x^3-x$ (which is not a function, even when restricted to $[-1,0]\cup[1,\infty)$, because there are two $y$ values for each $x$ value).
This graph is disconnected; more specifically, it consists of two connected components. This is a general topological concept that can be applied to all sets, not just to graphs of relations.