Question Video: The Relation between the Domain and Range of Functions | Nagwa Question Video: The Relation between the Domain and Range of Functions | Nagwa

# Question Video: The Relation between the Domain and Range of Functions Mathematics • Third Year of Preparatory School

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If π is a function from the set π to the set π, what do we call π?

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### Video Transcript

If π is a function from the set π to the set π, what do we call π?

Remember, a function is a special type of relation or mapping that maps elements from one set onto exactly one element in the second set. In this case, our function π maps elements from the set π to the set π. If we say that lowercase π₯ is some element of set π and lowercase π¦ is some element in set π, then we can represent this by saying π¦ is equal to π of π₯; π¦ is some function of π₯. And when we think about functions, there are two special words we use to describe the relevant sets.

The elements in set π , which weβve defined to be lowercase π₯, are all possible inputs to the function. And the elements in set π, which weβve defined to be lowercase π¦, are all possible outputs. And when we think about the set of possible inputs of a function, weβre thinking about the domain of the function, whilst when we think about the set of possible outputs, weβre thinking about its range.

The question asks us here βwhat do we call π?β Since π is the set of possible inputs for our function π, then π is the domain of the function.

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