To determine which of the given choices represents a function, we need to recall the definition of a function:
A function is a relation in which each input (x value) has exactly one unique output (y value).
Let's evaluate the given options:
### Option B:
[tex]\[
\{(-1,-11),(0,-7),(1,-3),(-1,5),(2,0)\}
\][/tex]
For this set to be a function, each x value should correspond to exactly one y value.
- Here, [tex]\( x = -1 \)[/tex] corresponds to both [tex]\( y = -11 \)[/tex] and [tex]\( y = 5 \)[/tex].
- Since [tex]\( x = -1 \)[/tex] has two different y values, this set is not a function.
### Option D:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline$x$ & -18 & -13 & 3 & 5 & -6 & 3 \\
\hline$y$ & -7 & -2 & 14 & 16 & 5 & 19 \\
\hline
\end{tabular}
\][/tex]
For this table to represent a function, each x value should map to exactly one y value.
- Here, [tex]\( x = 3 \)[/tex] corresponds to both [tex]\( y = 14 \)[/tex] and [tex]\( y = 19 \)[/tex].
- Since [tex]\( x = 3 \)[/tex] has two different y values, this table is not a function.
Since both Option B and Option D do not satisfy the conditions of a function, none of the provided options represent a function.
Thus, the correct answer is:
[tex]\[
-1
\][/tex]
