Final answer:
The relation { (11, 4), (0, 5), (11, -6), (-5, 8) } is not a function because the x-value 11 maps to two different y-values, which violates the definition of a function.
Step-by-step explanation:
The relation given is { (11, 4), (0, 5), (11, -6), (-5, 8) }. To determine whether this relation is a function, we need to look for unique x-values. A relation is a function if for each x-value, there is only one unique y-value associated with it. In this relation, the x-value 11 is associated with two different y-values (4 and -6). Therefore, because the same x-value maps to more than one y-value, this relation is not a function.