It depends on what your understanding of publisher_city actually is. For an attribute to be functionally dependant on another attribute (lets use P and C, for publisher and publisher_city) then for each value of P there must only be one value of C, for that P value (note there can be lots of different P values) So in this case P -> C, or C is functionally dependant on P if

Publisher (P) City (C)

Penguin London

Darby London

Horst New York

If however Penguin had London for some values of C and New York for others, then C would not be functionally dependant on P.

Quick edit, you might want to look at Publisher and title there as well.