The relation {(2, 11), (-9, 8), (14, 1), (5, 5)} is not a function when which ordered pair is added to the set? (8, -9) (6, 11) (0, 0) (2, 18)

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Borys Shumyatskiy eNotes educator| Certified Educator

Hello!

In these ordered pairs the first element (number) is an argument, and the second is the corresponding value. For this relation to be a function (which means one-valued function), each argument must have only one corresponding value.

This given relation has four arguments: `2,` `-9,` `4` and `5,` and they are all different. So now it is a (one-valued) function. To make this relation not a one-valued function, we have to add a pair which has an argument coinciding with one of these four and a different value for this argument.

The only suitable pair is (2, 18). It gives a different value (18 instead of 11) for the same argument (2).

sroessler | Student

A set of ordered pairs is a function if each domain value is only paired with one range value. That means each x-value can only match with one y-value. In other words, there is only one possible y-value that can go with any x-value.

Right now, those four sets of ordered pairs are a function because they all have different x-values, so there are no repeated x-values. However, if we added the point (2, 18) to the set, we'd have two points with the same x-value. (2, 11) and (2, 18) both have an x-value of 2, but one is paired with 11 and the other is paired with 18. In this case, there are two possible y-values that go with the x-value 2, so it is no longer a function.

The relation is not a function when the point (2, 18) is added to the set.