Real-valued function and extended-real-valued function, what's the difference?

This might be a simple question, but it is really confusing. I have not found any explicit definition or example of extended real-valued function.

My guess is that f defined by f: x -> 1/x on (0,1) is REAl-valued, while g defined by g: x -> 1/x on [0,1) is EXTENDED REAL-valued. Is this the case?

Could someone please give some examples?