'function-based' is a modern English compound formed from 'function' + past participle 'based'. 'Function' ultimately comes from Latin 'functio' (from 'fungi', meaning 'to perform, execute'), and 'base' comes via Old French and Latin 'basis' meaning 'foundation'.

'Function' entered English via Medieval/Modern Latin 'functio' (from Latin 'fungi') and became established in Middle/Modern English as 'function'. 'Base' entered English from Old French (and Latin 'basis'). Combining a noun with the past participle 'based' to form adjectives (e.g., 'X-based') is a common modern English formation, so 'function-based' arose as a straightforward compound in recent English usage.

Individually, 'function' originally meant 'performance' or 'execution', and 'base' meant 'foundation'. Together in the compound they came to mean 'having its basis in function'—a usage consistent with modern senses emphasizing organization or design according to purpose.