The prepositional phrase functions as an adjective in the following sentence: The man with a fancy yellow hat rode an old (...).
Explanation:
A preposition is a word that expresses a relationship between a noun and a pronoun and another word in a sentence. Prepositional phrases can function in three ways: as a noun, as an adjective, or as an adverb. In this case, the prepositional phrase is functioning as an adjective, so it is giving us additional information about a noun and a pronoun in the sentence. It is stating which one or which kind. In the sentence above, it is specifying which man the speaker is talking about, it helps identify the man. It is not only the man, but the man with the fancy yellow hat. The head of the PP is the preposition "with".