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The points represented are:
The domain is the set of all the inputs, i.e. the set composed by the x-coordinates of these points.
The range is the set of all the outputs, i.e. the set composed by the y-coordinates of these points.
This relation is a function, because you never map two outputs for the same input (i.e. you don't have two points with the same x-coordinate, but different y-coordinates).