Which of the following values could be used for x and would cause the following relation to NOT be a function?
{(2,3), (-2,6), (3,-4), (x, 2), (5,-9)}
x=6
x=6
x=0
x=0
x=3
x=3
x=-4
None of the given values for x would cause the relation to NOT be a function.
In order for a relation to be a function, each input (x-value) must have only one output (y-value). In the given relation, there is no repetition of x-values, so all of the values for x would work and the relation remains a function.
In order for the relation to NOT be a function, there must be more than one y-value corresponding to a given x-value. Let's test each of the values of x provided to see if any of them cause the relation to not be a function.
1. x = 6:
If we substitute x = 6 into the relation, we get (6, 2). Since there is only one y-value (2) for this x-value, the relation remains a function.
2. x = 0:
If we substitute x = 0 into the relation, we get (0, 2). Again, there is only one y-value (2) for this x-value, so the relation remains a function.
3. x = 3:
If we substitute x = 3 into the relation, we get (3, 2). Once again, there is only one y-value (2) for this x-value, so the relation remains a function.
4. x = -4:
If we substitute x = -4 into the relation, we get (-4, 2). As before, there is only one y-value (2) for this x-value, so the relation remains a function.
In summary, none of the provided values for x (6, 0, 3, -4) cause the given relation to not be a function.
To determine whether the given relation is a function or not, we need to check if there are any duplicate x-values with different y-values. If there are such duplicates, then the relation is not a function.
Let's go through each possible value of x and check if it creates a duplicate x-value in the relation:
For x = 6: This value of x does not exist in the original relation, so it will not create a duplicate x-value.
For x = 0: Again, this value of x does not exist in the original relation, so it will not create a duplicate x-value.
For x = 3: This value of x already exists in the original relation as (3, -4). This means that if we add another point with x = 3, it will create a duplicate x-value with different y-values. Therefore, choosing x = 3 would cause the relation to not be a function.
For x = -4: This value of x also already exists in the original relation as (-2, 6). Adding another point with x = -4 would result in a duplicate x-value with different y-values. So, choosing x = -4 would also cause the relation to not be a function.
In summary, the values of x that would cause the relation to NOT be a function are x = 3 and x = -4.