To determine whether a relation is a function, we need to check if each input (first element of the pairs) in the relation is associated with exactly one output (second element of the pairs).
Consider the given relation B: [tex]\[ \{(-8, 8), (-6, 5), (-6, 4), (-3, 1), (-1, 0)\} \][/tex]
Let's go through each pair in the relation and track the inputs and their corresponding outputs:
1. The input [tex]\(-8\)[/tex] is associated with the output [tex]\(8\)[/tex].
2. The input [tex]\(-6\)[/tex] is associated with the output [tex]\(5\)[/tex].
3. The input [tex]\(-6\)[/tex] is also associated with the output [tex]\(4\)[/tex].
4. The input [tex]\(-3\)[/tex] is associated with the output [tex]\(1\)[/tex].
5. The input [tex]\(-1\)[/tex] is associated with the output [tex]\(0\)[/tex].
We notice that the input [tex]\(-6\)[/tex] is associated with two different outputs: [tex]\(5\)[/tex] and [tex]\(4\)[/tex]. This means that the input [tex]\(-6\)[/tex] does not have a unique output.
Because there exists at least one input that is mapped to multiple outputs, the given relation [tex]\[ \{(-8, 8), (-6, 5), (-6, 4), (-3, 1), (-1, 0)\} \][/tex] is not a function.
Therefore, the answer is that relation B is not a function.
