To determine which of the given sets represents a function, we need to make sure that each input (or [tex]\( x \)[/tex]-value) corresponds to exactly one output (or [tex]\( y \)[/tex]-value). In other words, there should be no repeated [tex]\( x \)[/tex]-values in the set of ordered pairs.
Let's analyze each option:
### Option B: [tex]\(\{(-1, -11), (0, -7), (1, -3), (-1, 5), (2, 0)\}\)[/tex]
In the set [tex]\(\{(-1, -11), (0, -7), (1, -3), (-1, 5), (2, 0)\}\)[/tex], we have the following pairs:
- [tex]\((-1, -11)\)[/tex]
- [tex]\((0, -7)\)[/tex]
- [tex]\((1, -3)\)[/tex]
- [tex]\((-1, 5)\)[/tex]
- [tex]\((2, 0)\)[/tex]
Notice that the [tex]\( x \)[/tex]-value [tex]\(-1\)[/tex] is repeated, appearing in both [tex]\((-1, -11)\)[/tex] and [tex]\((-1, 5)\)[/tex]. This indicates that there are two different [tex]\( y \)[/tex]-values associated with the same [tex]\( x \)[/tex]-value [tex]\(-1\)[/tex]. Therefore, this set [tex]\(\{(-1, -11), (0, -7), (1, -3), (-1, 5), (2, 0)\}\)[/tex] does not represent a function.
### Option D:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & -18 & -13 & 3 & 5 & -6 & 3 \\
\hline
y & -7 & -2 & 14 & 16 & 5 & 19 \\
\hline
\end{array}
\][/tex]
In this table, we have the following [tex]\( x \)[/tex]-values: [tex]\(-18, -13, 3, 5, -6, 3\)[/tex].
Notice that the [tex]\( x \)[/tex]-value [tex]\( 3 \)[/tex] is repeated, appearing twice (once with [tex]\( y = 14 \)[/tex] and once with [tex]\( y = 19 \)[/tex]). This indicates that there are two different [tex]\( y \)[/tex]-values associated with the same [tex]\( x \)[/tex]-value [tex]\( 3 \)[/tex]. Therefore, this set also does not represent a function.
### Conclusion
Given that both Option B and Option D contain repeated [tex]\( x \)[/tex]-values, neither represents a function. Thus, the correct answer is that none of the given sets represent a function.
Therefore, the result is:
[tex]\[
0
\][/tex]
