Learn English – Is “who” singular or plural

With What questions, the verb must have the same number as the following noun or noun phrase, so the two correct versions are the first and the third:

What is their function? ... Here you are asking about one function and must use is.

What are their functions? ... Here you are asking about multiple functions and must use are.

Think about the answer you will get—the question must use the same verb:

Their function is this ...

Their functions are these ...

What may be confusing you is the plural their, which implies that you are asking about the function or functions of multiple things. Which of these two questions you ask will depend on the context:

What is their function? ... Here you are looking at several tools or officials or rules or whatever and assuming that they all have the same function, so you ask about a singular function.

What are their functions? ... Here you are looking at several tools or officials or rules and assuming that each has a different function, so you ask about plural functions.

Likewise, you may use these same to forms with just a single thing:

What is its function? ... Here you are looking at one thing and assuming it has only one function.

What are its functions? ... Here you are looking at one thing and assuming it has multiple functions.

Who can be either an interrogative pronoun ("Who is that?") or a relative pronoun ("The man who sells fruit"). Neither interrogative pronouns (question words) nor relative pronouns (which/that/who and variations) are bound to grammatical number by themselves. The plurality is instead bound to the object in question.

Examples:

"Who is that man?" - singular due to "man"

"Who are those people?" - plural due to "people"

"The man, who is sitting there,..." - again singular due to "man"

"The men, who are sitting there,..." - plural due to "men"