Final answer:
The infinitive 'to apologize' in the sentence 'Damian called to apologize for missing the basketball game last night' functions as an adverb, providing the reason why Damian called.
Step-by-step explanation:
The correct answer to the question regarding the use of the infinitive in the sentence 'Damian called to apologize for missing the basketball game last night' is D. The infinitive to apologize functions as an adverb that modifies the verb called.
An infinitive is the base form of a verb, often preceded by 'to.' In this instance, 'to apologize' tells us 'why' Damian called. It does not function as a subject or an adjective. Rather, it is providing more information about the purpose of the action taken by Damian, which characterizes it as modifying the verb and therefore acting adverbially.