How is the underlined prepositional phrase used in the sentence?

hearing the key in the lock, the delighted dog dashed to the front door.

a. as a adjectival phrase
b. as a adverbial phrase
c. as a noun phrase
d. as a verb phrase

The answer is B: As an Adverbial Prase.   A Prepositional Phrase includes a preposition, its object and its modifiers. The Prepositional Phrases can function as adverbial phrases or adjective phrases to modify other words in the sentence. In the example, " Hearing the key in the lock" and "...dashed to the front door." in and to are prepositions that are used to form the two prepositional phrases: "in the lock" and "to the front door."

The underlined prepositional phrase "to the front door" is used in the sentence as an adverbial phrase

Explanation:

This example is following one of the structures to make an adverbial phrase, which starts with a preposition (in this case "to") the phrase together can be considered an adverb of place, the other three options are not correct because they require different elements in the structure to be considered that kind of phrase.

the krebs cycle and electron transport occur in the mitochondria, though other than that i would need to know more information.

learning how to embrace the effects of colonialism is one of the central ideas of the play.