Let's analyze each option given to determine if it represents a function. A set of ordered pairs represents a function if each input (x-value) is mapped to exactly one output (y-value). This means that no x-value can be associated with more than one y-value.
Let's break down each option individually:
### Option A
No information is provided, so it cannot be analyzed.
### Option B: [tex]$\{(-1,-11),(0,-7),(1,-3),(-1,5),(2,0)\}$[/tex]
In this set of ordered pairs, we have:
[tex]\[
\begin{align*}
(-1, -11), \\
(0, -7), \\
(1, -3), \\
(-1, 5), \\
(2, 0)
\end{align*}
\][/tex]
- The x-value [tex]\( -1 \)[/tex] is paired with both [tex]\( -11 \)[/tex] and [tex]\( 5 \)[/tex].
Since the x-value [tex]\( -1 \)[/tex] is associated with two different y-values ([tex]\(-11\)[/tex] and 5), this set of ordered pairs does not represent a function.
### Option C
[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]
We observe the following pairs:
[tex]\[
\begin{align*}
(-18, -7), \\
(-13, -2), \\
(3, 14), \\
(5, 16), \\
(-6, 5), \\
(3, 19)
\end{align*}
\][/tex]
- The x-value [tex]\( 3 \)[/tex] is paired with both [tex]\( 14 \)[/tex] and [tex]\( 19 \)[/tex].
Since the x-value [tex]\( 3 \)[/tex] is associated with two different y-values ([tex]\(14\)[/tex] and [tex]\(19\)[/tex]), this set of ordered pairs does not represent a function.
### Option D
No information is provided, so it cannot be analyzed.
### Summary
Based on the analysis, Option B does not represent a function because there is a repeated x-value associated with different y-values. This is confirmed by finding that the x-value [tex]\(-1\)[/tex] is paired with both [tex]\(-11\)[/tex] and [tex]\(5\)[/tex], which violates the definition of a function.
Therefore, among the provided options, Option B does not represent a function.
