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)}
Any value of x that already appears in the relation would cause the relation to not be a function.
Thus, if x = 2, -2, 3, or 5, the relation would not be a function.
To determine if a relation is a function, we need to check if every x-value is paired with only one y-value.
In this case, if there is any repeated x-value with different y-values or vice versa, the relation will not be a function.
Let's examine the given relation: {(2,3), (-2,6), (3,-4), (x, 2), (5,-9)}.
The x-value that could cause the relation to NOT be a function is the same value as one of the other x-values in the relation.
In this case, we have an x-value of 2 in the relation. Since we already have the point (2,3), having another point with the x-value of 2 would cause the relation to not be a function.
Therefore, if x = 2, the relation would NOT be a function.
To determine if the given relation is a function, we need to check if every x-value has a unique corresponding y-value. In other words, no two ordered pairs can have the same x-value.
In the given relation {(2,3), (-2,6), (3,-4), (x, 2), (5,-9)}, all the ordered pairs have unique x-values except for the pair (x, 2). For this relation to be a function, the value of x cannot be any value that has already been used in the relation.
By examining the other ordered pairs, we see that the x-values used so far are 2, -2, 3, and 5. Therefore, any value for x that is equal to or even a combination of these values would cause the relation to not be a function.
For example, if x = 2, (-2, 6) and (x, 2) would have the same x-value, violating the definition of a function. Similarly, if x = -2, (2, 3) and (x, 2) would have the same x-value. The same applies for x = 3 and x = 5.
To summarize, any value for x that is equal to or a combination of 2, -2, 3, or 5 would cause the relation to NOT be a function.