Latin word functio comes from Proto-Indo-European *bʰewgʰ-

Detailed word origin of functio

Dictionary entry	Language	Definition
*bʰewgʰ-	Proto-Indo-European (ine-pro)
fungor	Latin (lat)	I finish (something), complete (something), end (something). I perform, execute, administer, discharge, observe.
functus	Latin (lat)
functio	Latin (lat)	(mathematics) function. Performance, execution (of a task).

Words with the same origin as functio