Bad European function (4)
I believe the answer is:
sine
'function' is the definition.
(mathematical function)
'bad european' is the wordplay.
'bad' becomes 'sin' ().
'european' becomes 'E' (abbreviation e.g. EU).
'sin'+'e'='SINE'
(Other definitions for sine that I've seen before include "Indefinitely, with no appointed date - . . . . die" , "Trig function" , "Mathematical function" , "Opposite/hypoteneuse" , "Without; maths function" .)