In a relation to be classified as a function, each input (x-value) must correspond to exactly one output (y-value). This means that no two distinct pairs can have the same x-value.
In the given relation \({(2, 8), (4, 5), (7, 3), (9, 0), (?, 6)}\), we need to examine the x-values currently present: 2, 4, 7, and 9.
The missing x-value represented by "?" cannot be any of these existing x-values (2, 4, 7, or 9) because that would mean that the same x-value corresponds to two different outputs, which violates the definition of a function.
Therefore, the value that is not allowed for the missing x-value is 2, 4, 7, or 9 (any of these values). Any of these existing x-values would not be allowed because it would make the relation not a function.
Concisely, the missing x-value cannot be 2, 4, 7, or 9.