Kenneth G. Wilson (1923). The Columbia Guide to Standard American English. 1993.
check 1 (v.)
is used in many combinations with prepositions alone and in clusters, and although some of these combinations may seem to tend toward the Informal and the Conversational, in fact almost all are Standard idioms: check on (Be sure to check on his luggage), check over (Just check over that menu, will you please?), check in (What time will you check in at your hotel?), check into (Do check into his references), check up (Check up to see if well have time to eat first), check up on (Ill check up on her performance), check out (His testimony checks out), check out of (When are you going to check out of your room?), check over (Ive checked over the lists, and they are correct), check around (Will you check around and see whether you can find a sitter?).