Determine the domain and range for the relation described by the table and so, what they want us to say, what they want us to figure out, when they say the domain what are all the possible inputs that we could put into, this case, a relation and later we'll see a function and so over here, i guess one way to think about it the inputs that this relationship is defined for and so you can view the x as the input so when x is -1, y is 3 when x is 3, y is -2 when x is 3, again, y is 2 that's why we can't describe this as a function here because we have two y values for a given x value but it can be a relation when x is 4, y is 8 when x is 6, y is -1 so to answer the first part, when they ask us what is the domain of this relation they're really just saying what are all of the inputs, what are all of the x values for which this relation is defined? and they list the x values over here so it is a set, and that is what these curly brackets mean that i'm about to describe a set it is the set of the numbers -1, 3, 4, and 6 so all we're saying here if we saying the domain of this relation is these 4 numbers it says that this relation is defined for any of these four numbers if you give any of these numbers as an x value there is a y, at least one y value associated with it now, when they talk about the range of this relation and the idea also applies to functions, which are a more specific class of relations you can view them as a well behaved relation the range is all the possible output that this relation can give you given the inputs, what are all the possible values that this relation can take on? so here you'll take a look at all the possible y values that this relation can take on we can write them in order, or we don't have to write them in order, but i'll just write them in order actually let's just go straight this way a set does not imply some type of order, it just means a collection of things so the range here, well our y value can take on the value 3, it can take on the value 2, it can take on the value 8, and it can take on the value -1 and we're done! these are the x values for which this relation is defined then you can actually find an association or relationship and these are all the y values these are kind of all the outputs of the relation that it can take on we just look right over here to find them