What is an infinitive verb? In a simple sentence like "Teachers taught..." How would I expand it by beginning with an infinitive verb?

Example: To teach students is the teachers' main responsibility.

Infinitive is an example of a verbal or fake verb. You can easily identify it in a sentences for it uses the formula to + base form of the verb.* Examples are to see, to talk, to walk, to look, to post. *

For further explanation, let's have its functions.

##1.## Noun - an infinitive functioning as a noun is the subject of the sentence or what is being talked about.

Example: To walk a mile is one of the challenges I want to do.

Question: What is one of the challenges that I want to do? Answer: To walk a mile.

*It is usually found at the beginning of the sentence.\

##2.## Adjective - when an infinitive describes a subject or something in a sentence; it is mostly found after a noun.

Example: You only have five minutes to think.

Does the sentence have an action word in which you see movement? NONE.*

What word comes before the infinitive to think? FIVE MINUTES

Five minutes is what part of speech? A NOUN*

What word is being described by the word phrase to think? *FIVE MINUTES

Therefore, "to think" in the sentence is an adjective.

##3.## Adverb- modifies or comes AFTER THE VERB.

Example: We live in this world to serve God.

Does the sentence have an action word in which you see movement? YES, IT DOES.*

What word comes before the infinitive to serve? live in this world/ LIVE

"Live" is what part of speech? A VERB*

What word is being described by the word phrase to serve? *LIVE

Therefore, "to serve" in the sentence is an adverb for it comes after the verb meaning IT MODIFIES THE VERB.

Hope it helps.