Answer:
Prepositional phrase: to attend a club meeting.
Use: used as an adverbial phrase or used as an adverb.
Step-by-step explanation:
Prepositional phrases are those phrases or groups of words that contain a preposition and modifies the noun or verb in the sentence. Such phrases contain or start with prepositions and may be termed as adverbial phrases or adjectival, depending on what they are used for or what they are modifying.
In the given sentence "I stayed late to attend a club meeting after school", the prepositional phrase is "to attend a club meeting". This is easy to identify for the phrase starts with the preposition "to". Also, the phrase is an adverbial phrase for it acts as a modifier of the verb "stayed late".