How can the word “no” be an adverb?

I am an English teacher and keen to learn things in detail to explain to my students. I would like a detailed explanation of why the word “no” can be an adverb if it is being used alone in response to some question. It is not qualifying anything in this usage.

'No' has many functions in sentences. Adverbial function is one among them. 'No' as a negative response to questions or requests is an adverb.

Examples: Are you ready? - No. ( = No, I am not ready. It modifies the adjective ready)

Did you forget? - No. (= No, I did not forget. It modifies the verb forget)

Can you speak English fluently? - No. (= No, not fluently )

'No' can also act as a noun, an adjective, a determiner etc.

Details and more examples can be had from Merriam Webster or any other dictionaries.