Answer:
1. An infinitive usually begins with the word “to” and is followed by the base form of a verb. Examples of infinitives include to read, to run, to jump, to play, to sing, to laugh, to cry, to eat, and to go.
2. In English grammar, an infinitive phrase is a verbal construction made up of the particle to and the base form of a verb, with or without modifiers, complements, and objects. Also called an infinitival phrase and a to-infinitive phrase.
3. Infinitive phrases include infinitives. ... Examples include, “to walk,” “to read,” or “to eat.” Infinitives can act as nouns, adjectives, or adverbs. As a noun, they might act as the subject of the sentence. For example, “To travel is the only thing on her mind.” As an adjective, they'll modify a noun.
4. To study advanced math Adjective modifying “math”
To eat a giant sandwich Adjective modifying “sandwich”
To play guitar beautifully Adverb modifying “to play”
To leave the party quietly Adverb modifying “to leave”