For a relation to be considered a function, each input (x-value) must correspond to exactly one output (y-value). This means that no two different inputs can have the same output.
In the table you provided, we have the following x-values:
- -1
- -2
- a
- -3
If we want the relation to not represent a function, we need the value of \( a \) to be such that it matches one of the existing x-values, which would create a situation where one input (the repeated x-value) corresponds to multiple outputs (potentially).
The existing x-values are -1, -2, and -3. Therefore, if \( a \) takes on one of these values, the relation will not be a function.
Thus, the possible values of \( a \) that would result in the table NOT representing a function are:
- \( a = -1 \)
- \( a = -2 \)
- \( a = -3 \)
Any of these values will satisfy the condition. Therefore, the answer is:
\( a = -1 \), \( a = -2 \), or \( a = -3 \).
1 answer