Answer:
Infinitive: to swim
Use: noun predicate or predicate nominative
Step-by-step explanation:
The infinitive is the basic form of a verb, that is, a form with no inflections - no changes due to a relationship with a subject. It usually comes preceded by "to".
In the sentence "Her ambition is to swim gracefully", the infinitive is "to swim". It functions as a noun would and, in this particular sentence, it is a predicate nominative. A predicate noun or predicate nominative is a noun or noun phrase that comes after a liking verb (such as "to be") and has the purpose of providing further information about the subject of the sentence. Predicate nouns do not follow action verbs, since they don't express actions, but states of being. "To swim" is providing further information about "her ambition".