Question Video: The Relation between the Domain and Range of Functions Mathematics • 8th Grade

If 𝑓 is a function from the set 𝑋 to the set π‘Œ, what do we call 𝑋?

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Video Transcript

If 𝑓 is a function from the set 𝑋 to the set π‘Œ, what do we call 𝑋?

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 𝑓 maps elements from the set 𝑋 to the set π‘Œ. If we say that lowercase π‘₯ is some element of set 𝑋 and lowercase 𝑦 is some element in set π‘Œ, then we can represent this by saying 𝑦 is equal to 𝑓 of π‘₯; 𝑦 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 𝑋 , which we’ve defined to be lowercase π‘₯, are all possible inputs to the function. And the elements in set π‘Œ, which we’ve defined to be lowercase 𝑦, are all possible outputs. And when we think about the set of possible inputs of a function, we’re thinking about the domain of the function, whilst when we think about the set of possible outputs, we’re thinking about its range.

The question asks us here β€œwhat do we call 𝑋?” Since 𝑋 is the set of possible inputs for our function 𝑓, then 𝑋 is the domain of the function.

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