Final answer:
The phrase "for running" could function as an adverbial phrase or part of a gerund phrase depending on the sentence context. It generally indicates purpose or reason when modifying verbs, adjectives, or adverbs, but without more information, the specific classification of this phrase cannot be determined unequivocally.
Step-by-step explanation:
The phrase "for running" can serve various functions in a sentence, depending on the context. However, without additional context, we cannot definitively classify it. Yet, if we analyze common uses, the phrase "for running" could be part of a prepositional phrase that acts as an adverbial phrase, modifying a verb, adjective, or an adverb to indicate purpose or reason for an action.
For example, in the sentence 'She wears special shoes for running,' the phrase "for running" explains why she wears the shoes, which qualifies as an adverbial usage. Likewise, "for running" could be part of a larger phrase such as a gerund phrase ('My reason for running the marathon is personal'), where "running" is a gerund functioning as a noun, and the whole phrase "for running the marathon" acts as a noun phrase serving as the subject complement.
Understanding the role of phrases like "for running" requires analyzing them within their sentences. Phrases are versatile and their function can shift between adverbial, adjectival, and nominal forms. Hence, identifying the use of a phrase involves looking at what the phrase modifies or complements in the context of the sentence it is part of.