What I am trying to get at is the sort of initial assessment of a function, or in other words, the line of reasoning employed before any calculations, that leads to the conclusion that an asymptote of such and such a kind is present.
From what I gather, an asymptote is a value which the function never reaches, it only “approaches” it. But the connection between this idea and a mathematical expression is veiled in darkness, so likewise are the procedures—although I can perform them.
I apologize for the perhaps broad or vague question. My ignorance is such that I cannot see exactly what it is that confuses me, and so I cannot formulate a more precise question.