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)}
Responses
x=3
x=3
x=0
x=0
x=-4
x=-4
x=6
x=6
In order for the relation to NOT be a function, there must be multiple outputs for the same input. Let's check the options:
- If x = 3, the relation would have two outputs for x = 3: (3, -4) and (3, 2). Therefore, x = 3 would cause the relation to NOT be a function.
- If x = 0, the relation only has one output for x = 0: (0, 2). Therefore, x = 0 would not cause the relation to NOT be a function.
- If x = -4, the relation only has one output for x = -4: (-4, 6). Therefore, x = -4 would not cause the relation to NOT be a function.
- If x = 6, the relation only has one output for x = 6: (6, 2). Therefore, x = 6 would not cause the relation to NOT be a function.
Therefore, the value x = 3 is the only value that would cause the given relation to NOT be a function.
To determine which value for x would cause the given relation to not be a function, we need to check if there are any duplicate x-values in the relation. In a function, each input (or x-value) should have only one corresponding output (or y-value).
Looking at the given relation:
{(2,3), (-2,6), (3,-4), (x, 2), (5,-9)}
We can see that there is already an x-value of 3, so if we choose x=3 again, it would result in a duplicate x-value. Therefore, x=3 is not a valid choice.
Similarly, we can see that x=0 and x=-4 are already present in the relation. Therefore, these values are also not valid choices.
However, the value x=6 is not present in the relation, so it can be used and would not cause the relation to be not a function.
In conclusion, the answer is x=6.