In which sentence does the underlined infinitive phrase function as a subject? The goal of the new train station is to move more
trains from the station to the city. The commuters were excited to ride on the new high-speed trains. To quickly move large groups of people is the purpose of public transportation.
The sentence in which the underlined infinitive phrase functions as a subject is the last one - to quickly move large groups of people is the purpose of public transportation. <em>To quickly move </em>is the infinitive phrase, and it is a subject.
The answer to your question would be that the sentence in which the underlined infinitive phrase functions as the subject is the following one: To quickly move large groups of people is the purpose of public transportation.
An infinitive clause is a subordinate clause whose verb is in this infinitive form. Moreover, they are not introduced by a subordinating conjunction.