To determine if a given set of ordered pairs represents a function, we need to check whether each input (x-value) maps to exactly one output (y-value). In other words, for a set to represent a function, each x-value in the set should appear only once.
Let's analyze option B:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 5 & -5 & 10 & 5 & -10 \\
\hline
\end{array}
\][/tex]
In this case, we have the following x-values: [tex]\(5, -5, 10, 5, -10\)[/tex].
Upon examining these x-values:
1. The x-value 5 appears twice.
2. Because the x-value 5 is duplicated, it means that it's possible for this value to map to two different outputs (although the outputs are not given, the duplication alone invalidates it as a function).
Therefore, since the x-value of 5 appears more than once, the relation cannot be considered a function. Each x-value must be unique for it to be a function, and this is not the case here.
Thus, the correct answer would be: This relation does not represent a function.
