5.Functions of the infinitive in the sentence.

The inf. functioning as subject may either precede the predicate or follow it. In the latter case it is introduced by the so-called introductory It , which is placed at the beginning of the sentence. F.e. To read is useful. It is everyone’s duty to attend classes.
As a predicative it is used after link verb “to be”. F.e. All I need is to be left alone. Can be introduced by the conj. [how, what, whom, when, where]. F.e. The question is what to do.
Part of a compound verbal(CV) predicate

Part of a CV modal predicate – after modal verbs and verbs, denoting modality[had better, would rather, would sooner, rather than]. F.e. You should do your homework.
Part of a CV aspect predicate – after verbs denoting beginning/continuation of an action[to begin, to start, to continue, to finish, to cease]. F.e. He began to work.

Object. F.e. I hope to see you today.
Attribute. F.e. There’s every reason to believe him; years to come; I have something to tell you.
Adverbial modifier:

of purpose – the inf. can be introduced by [in order to do/so as to do]. F.e. Sometimes you retreat in order to advance.
of result – usually occurs after adjectives. Conj-s[enough, too, sufficiently, quite, such as, so as]. F.e. I was too busy to see you. He came to Africa to die.
of comparison(manner) – [as if, as though]. F.e. She moved her hand as if to stop him.

Parenthesis – to tell you the truth, to make matters worse, so to speak, so to say, to be more exact, to be frank etc.