After the game we went to a dance at the youth center 1 complex sentence 2 compound sentence 3 sentence fragment 4 simple sentence

1. Complex sentence.

Explanation:

The sentence -

After the game we went to a dance at the youth center,

is a complex sentence. Complex sentences contains both an independent clause and a dependent clause. Independent clauses are those groups of words that can stand on their own and make complete sentence, while dependent clauses are not capable of standing on their own. Thus, the above sentence is a complex sentence for,

After the game (dependent clause) we went to a dance at the youth center (independent clause).

It cannot be a compound sentence for it has just one subject or predicate nor can it be a simple sentence for it contains more than one clause. Also, it is not a sentence fragment for it contains a whole sentence. thus, the correct answer is complex sentence.