Final answer:
The sentence with an infinitive phrase is 'They went to study math,' with the phrase functioning adverbially to modify 'went.'
Step-by-step explanation:
The sentence containing an infinitive phrase is "They went to study math." An infinitive phrase consists of the infinitive, which is the base form of a verb preceded by the word to, and can act nominally, adverbially, or adjectivally. In this sentence, to study is the infinitive and math is the direct object of the infinitive, making the entire phrase function adverbially to modify the verb went.
Infinitive phrases can be positioned in various parts of a sentence and can serve different grammatical functions. For example, they can be subjects, direct objects, or modifiers of nouns and verbs. It's important to identify how the infinitive phrase is functioning within the context of the sentence.