In the sentence

"Yellowstone National Park is one of the largest national parks in the U.S."

is the prepositional "of the largest national parks" modifying "one"? If so, is the prep phrase being used as an adjective or adverb. I say "adverb" because "is" is a linking verb, therefore "one" is a predicate noun", thus "of the largest national parks" is modifying an adjective, which makes it an adverb prep phrase, My book says the answer is adjective - why?

This phrase is an adjective phrase because (as you said) it modifies "one." In this sentence "one" is a predicate pronoun, thus its modifiers are adjectives.

To determine whether the prepositional phrase "of the largest national parks" is functioning as an adjective or an adverb in the given sentence, we need to further analyze how it is relating to "one."

In the sentence, "Yellowstone National Park is one of the largest national parks in the U.S.," the prepositional phrase "of the largest national parks" is modifying the noun "one." This phrase provides additional information about what type of "one" is being referred to.

To determine whether the prepositional phrase is acting as an adjective or adverb, we need to consider what it is modifying. Since "one" is a noun complement in this sentence (a predicate noun), the prepositional phrase is functioning as an adjective, not an adverb.

Adjective phrases modify nouns or pronouns, while adverb phrases modify verbs, adjectives, or adverbs. In this case, the prepositional phrase is describing the noun "one," indicating that it is part of a larger group of national parks. Thus, it is functioning as an adjective phrase.

To determine whether the prepositional phrase "of the largest national parks" is modifying the noun "one" or the adjective "largest," we need to consider the function of the phrase in the sentence.

In the given sentence, the phrase "of the largest national parks" is providing additional information about "Yellowstone National Park." This information is specifying the category to which Yellowstone National Park belongs. It tells us that Yellowstone National Park is one belonging to the category of "largest national parks."

Now, let's break down the structure of the sentence. "Yellowstone National Park" is the subject, and "is" is the linking verb. The complement of the verb "is" is the predicate noun "one." This means that "one" is functioning as a noun, not an adjective.

Since the prepositional phrase "of the largest national parks" is providing information about the noun "one," and not modifying an adjective, it is acting as an adjective phrase here. It describes the category or type of national park that Yellowstone National Park belongs to.

Therefore, according to the traditional analysis, your book is correct in categorizing the prepositional phrase as an adjective phrase.