Identify the function of the italicized noun clause.

whether dad arrives in time for the game depends on his conference.

subject

direct object

predicate noun

object of a preposition

appositive

Subject

Explanation:

Noun clause is a dependent clause which functions as a noun; it can be subject, direct object, indirect object, and object of preposition. Noun clause begins with connectors such as when, whether, why, who, where, etc.  

In this sentence Whether Dad arrives in time for the game is the noun clause which is the subject of the sentence.