Final answer:
A value of k that is the same as any x-value in the given pairs will make the relation not be a function. The options k = 8, k = -3, and k = 7 all match existing x-values, and thus would result in a violation of the definition of a function.
Step-by-step explanation:
A relation in mathematics is defined as a set of ordered pairs, and a function is a specific type of relation where every input (x-value) has exactly one output (y-value). Looking at the given pairs (8,5), (-3,4), (7,-2), and (k,0), if the value of k is the same as any x-value in the given pairs, the relation would not be a function because there would be multiple outputs for a single input.
Therefore, a value of k that would make the relation not a function should match one of the existing x-values in the pairs. The existing x-values are 8, -3, and 7. Accordingly, the possible values of k that would result in the relation not being a function are:
Options b) k = -3 and c) k = 7 match the x-values of the given pairs, so these would make the relation not a function. Option a) k = 8, which also matches an x-value, is an additional correct choice.