"Dysfunctional" vs. "disfunctional"

From WordReference.com on Dysfunction vs. Disfunction:

dys- is a Greek prefix meaning "bad", "abnormal", "difficult", or "impaired".
dis- is a Latin prefix with none of the above meanings.

dys- has the right meaning, but function is a Latin word. Hence the confusion.

Latin dis- can mean "lack of", "not", "opposite of", "away from".

This all explains why something dys-functional has a bad or abnormal function, rather than a lack of function that dis-functional implies.

There is no rationale, it's just one of the countless quirks of natural language.

The dis- prefix comes from Latin, dys- from Greek. They have some overlap in meaning, and with -functional, both could be used.

Now, function has Latin roots, so disfunctional would make more sense, in the way that both prefix and suffix come from Latin. However, dysfunctional has come to be the more commonly used spelling, disregarding the different roots of prefix and suffix.

The Oxford English Dictionary records disfunctional as a variant spelling of (the more usual) dysfunctional.