Final answer:
None of the provided values of k make the relation S not be a function, as they all result in unique x-values in the ordered pairs, which is the required condition for a relation to be considered a function.
Step-by-step explanation:
The question asks for what value(s) of k will the relation not be a function. A relation is a function if each input (x-value) is paired with exactly one output (y-value). Therefore, in the set S=2-, we must ensure that no two ordered pairs have the same first component.
If k=1, the absolute value of (k+1) is 2, so the first component of the first ordered pair becomes 2-2=0. This does not give us a repeated x-value with (-6,7), so S is still a function. If k=0, the absolute value of (k+1) is 1, which gives us 2-1=1, and this value isn't present in the other ordered pair, so S remains a function. If k=-1, then (k+1) becomes zero, and the absolute value is still zero, resulting in the first component being 2-0=2; again, there's no conflict with the other ordered pair.
However, if k=-2, the absolute value of (k+1) is 1, because |-2+1|=|-1|=1. In this case, the first component of the first ordered pair is 2-1=1. Since this does not give us a duplicated x-value with the other ordered pair, the relation still qualifies as a function.
Thus, none of the provided values of k make the relation not a function, as they all result in unique x-values in the set S, satisfying the definition of a function.