Reference for Turing to many-one reductions
I'm pretty sure you can find this in the book Bounded Queries in Recursion Theory by Martin and Gasarch, but I don't have access to a copy now to check. 

(Your statement gives an upper bound of $2^f$; most of that book is about lower bounding such quantities, so the upper bound must be in there somewhere, probably very near the beginning.)

PS - I agree with M. Blaser's comment: you're basically talking about truth-table reductions without using that terminology.