The f-word in systems engineering

Functions play a major role when designing systems. Given this importance one would assume, that there is a clear understanding of what a function is. As it turns out, there are many competing definitions, some of them even contradicting each other. Maybe we should refer to it as the f-word.
Now, in model-based engineering with for example SysML you have to decide, which model element to use for the f‑word. Many practitioners use activities, and this is a seemingly obvious choice: Activities consume their inputs and produce outputs. Sometimes however, the obvious choice is misleading.
Of course, engineering doesn‘t profit from a battle about the one correct definition. If your interpretation of the f-word works for you, all is good. However, the choice of the element in a modeling language has implications, since the SysML does have an exact definition of the semantics (albeit semiformal).
Let‘s look at one popular method, that even has the word „functional“ in its name: Functional Architecture for Systems (FAS-method). It uses activities to represent the f-word. In this presentation, I want to propose a different element, that in my opinion captures better, what the method’s implicit definition for the f-word is. Could it be, that other methods use the same definition?
Such a claim needs to be backed up by a convincing example. I will provide one. Let’s see, whether I can convince you.