functional testing comes under black box.

Functional Testing comes under Black Box testing. Because 
tester does not know about the internal details of the 
program. Based up on the test cases he will test.

Yes functionality comes under Blackbox not in white box.

functional testing comes under black box testing as the 
tester need not know the internal code and logic of the 
application. But functionality can be tested by the coder 
also by executing their fuctional modules and suppliying 
the data. hence it proves that functionality can be tested 
in both ways.