The teacher asked the class to STAY put while she went to the office

Transitive verb

Intrasitive verb

Auxiliary verb

Linking verb

The phrasal verb "to stay put" (in bold) is an intransitive verb as it does not need or have an object.

The verb "ask" on the other hand is a transitive verb since it has an object, which in this case is "class". The object of a transitive verb can be a noun, a noun phrase or a pronoun.