Identify the italicized part of the sentence.

the ''capital'' of texas is austin.

subject
predicate
direct object
indirect object
predicate noun
predicate adjective

I just done this one in class and it's "SUBJECT"

the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.