Functions are assumed to live on the entire real line. There is no explicit facility to say that f(x) (or f(x,y)) only lives on a finite domain.
If you write code for a function, that code can have a test in it, to error out perhaps if the domain is exceeded, or you might choose to do anything else that seems appropriate to you. Perhaps issue a warning, an error, or truncate any points to the interval bounds. Nothing stops you from doing so. In fact, it is good programming practice to use error checks in your code. For example, suppose your function works only on real numbers, but a complex number is passed in, or inf, or NaN, or [].
But if you use other code, passing it a function, unless that code is enabled to deal with a finite interval, then no, you cannot make it magically know how to handle functions that live only on a finite domain. Sorry, but the derivest tools are not so equipped. That would have made things considerably more complicated for me to have written.
