Answer: The relation of two quantities is a function only when for each point in the domain, there is only one point associated on the codomain (or range).
this means that, for a point x in the domain; if f(x) = y1 and f(x) = y2, this means that y1 = y2.
then:
"The assignment of zip codes to residences"
here the domain is residences, and the range or codomain is the zip code.
Each residence only can have one zip code, and it depends on where it is located, so if the domain is residences, for each point in the domain, there is only one ZIP code associated in the codomain, so this can be represented with a function.
"The assignment of residences to zip codes."
here the domain is the zip codes, and the codomain is the residences.
There can be more than one residence with the same zip code; this means that if x is the zip code, you cant find the value of y, because there are many possible options, then this can not be modeled with a function.