Intensional functions are global

Here's a soft mathematical idea: an overlooked difference between extensionally and intensionally specified functions is that the former is simply not, or ill, specified on extensions of the domain, whereas the latter is defined. I.e., a way to understand what an intensional function is "more" than an extensional counter, is that it is automatically "globally" defined on future extensions / possible inputs. Or, maybe, intensional functions are also defined on erroneous /ill-typed input.