To determine under which condition the relation does not represent a function, we need to recall the definition of a function: a relation is a function if every input (x-value) is associated with exactly one output (y-value).
In the given relation, we have:
- For x = 0, y = 5
- For x = -1, y = 4
- For x = a, y = 3
- For x = 4, y = 2
The key here is to identify if the x-value associated with any output (y-value) already exists. If we set \( a \) to any x-value that has already been used (which is 0, -1, or 4), then we would have two y-values for the same x-value, thus violating the definition of a function.
The x-values that already exist are 0, -1, and 4.
If we set \( a = 0 \), then the output for 0 would be both 5 and 3, which would mean that the x-value 0 would have two different y-values (5 and 3).
Similarly, we can analyze other options:
- If \( a = -1 \), y would have two outputs: 4 and 3.
- If \( a = 4 \), it would have y-values of 2 and 3.
However, if we set \( a \) to 5 or 3, it won’t conflict with any existing x-values, meaning it will still be a valid function.
Therefore, in order for the relation NOT to represent a function, the value of \( a \) should be:
a = 0
This means the correct answer is:
0