Explanation

In the sentence "the book on the table is mine," the phrase "on the table" functions as a prepositional phrase that modifies the noun "book." This means it provides additional information about the book, specifically indicating its location.

In grammatical terms, modifiers like "on the table" can describe or limit a noun. While "on the table" itself is not an adjective, the entire phrase serves the purpose of describing which specific book we are discussingit's not just any book, but the one that is situated on the table.

Therefore, the key focus is on how this phrase operates within the context of the sentence. While "on the table" directly isn't an adjective, since it provides essential descriptive information about the noun “book,” it effectively performs the function typically associated with adjectives, which is to modify or give more detail about a noun. Hence, while "on the table" is a prepositional phrase, it concerns the modification and contextual specification akin to what an adjective does, making option B the best descriptor of its function in this context.