... but sometimes Cooper’s spirit <u>for his team</u> was not enough for a win.
Answer:
an adjectival phrase
Explanation:
The prepositional phrase <u>for his team</u> consists of the preposition <u>for</u> and the object of the preposition <u>his team</u>.
In a sentence, prepositional phrases can function in three ways: as a noun, as an adjective, or as an adverb.
If a prepositional phrase functions as an <em>adjective</em>, it is an adjectival phrase.
In this sentence, the preposition <u>for</u> is telling us the relationship between the <u>team</u> and the <u>spirit</u>. Since the word <u>spirit</u> is a noun, this is an adjectival phrase.
Once again:
the prepositional phrase <u>for his team</u> functions as an adjective because it modifies the noun <u>spirit</u>. It is an adjectival phrase.