Answer:
The sentence that includes an infinitive phrase used as a noun is:
A. My goal in this essay is to share my views about a favorite sport.
Step-by-step explanation:
There are two options with infinitive phrases: letters A and C. However, in letter C, the infinitive phrase "to watch" functions as an adjective, modifying "runner". Therefore, we can eliminate it. We are left with letter A. The infinitive phrase begins with "to share", and it comes after the linking verb "is". As we know, linking verbs can be completed with pronouns, nouns, adjectives - anything that gives information about the subject. In this case, the infinitive phrase completing the linking verb is functioning as a noun.