ok, so my answer is D. Seven function types. Final Answer.
(...waiting for the failure buzzer.....)
my thinking is there are the Built in functions plus these six others.
AF = Aggregate function (CLR) AGGREGATE_FUNCTION
FS = Assembly (CLR) scalar-function CLR_SCALAR_FUNCTION
FT = Assembly (CLR) table-valued function CLR_TABLE_VALUED_FUNCTION
IF = SQL inline table-valued function SQL_INLINE_TABLE_VALUED_FUNCTION
FN = SQL scalar function SQL_SCALAR_FUNCTION
TF = SQL table-valued-function SQL_TABLE_VALUED_FUNCTION
Lowell