I would rather be sleeping!
It is a gerund functioning as a noun.
It is a gerund functioning as a verb.
It is an infinitive functioning as a noun.
It is an infinitive functioning as a verb.

The correct answer is A: It is a gerund functioning as a noun.

Gerunds are words formed from verbs. They function as nouns and end in -ing. Gerunds are used in sentences that convey the meaning of real or complete actions.

On the contrary, infinitives are verb forms that do not end in -ing. They are formed with -to preceding the verb form. They are used in sentences that convey the meaning of unreal or future actions.

600 dollars if i'm not mistaken.