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Determine the domain and range for the relation described by the table

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and so, what they want us to say, what they want us to figure out, when they say the domain

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what are all the possible inputs that we could put into, this case, a relation

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and later we'll see a function

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and so over here, i guess one way to think about it

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the inputs that this relationship is defined for

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and so you can view the x as the input

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so when x is -1, y is 3

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when x is 3, y is -2

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when x is 3, again, y is 2

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that's why we can't describe this as a function

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here because we have two y values for a given x value

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but it can be a relation

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when x is 4, y is 8

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when x is 6, y is -1

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so to answer the first part, when they ask us what is the domain of this relation

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they're really just saying

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what are all of the inputs, what are all of the x values for which this relation is defined?

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and they list the x values over here

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so it is a set, and that is what these curly brackets mean

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that i'm about to describe a set

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it is the set of the numbers -1, 3, 4, and 6

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so all we're saying here

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if we saying the domain of this relation is these 4 numbers

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it says that this relation is defined for any of these four numbers

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if you give any of these numbers as an x value

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there is a y, at least one y value associated with it

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now, when they talk about the range of this relation

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and the idea also applies to functions, which are a more specific class of relations

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you can view them as a well behaved relation

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the range is all the possible output that this relation can give you

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given the inputs, what are all the possible values that this relation can take on?

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so here you'll take a look at all the possible y values that this relation can take on

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we can write them in order, or we don't have to write them in order, but i'll just write them in order

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actually let's just go straight this way

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a set does not imply some type of order, it just means a collection of things

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so the range here, well our y value can take on the value 3, it can take on the value 2, it can take

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on the value 8, and it can take on the value -1

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and we're done!

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these are the x values for which this relation is defined

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then you can actually find an association or relationship

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and these are all the y values

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these are kind of all the outputs of the relation that it can take on

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we just look right over here to find them