To determine which of the tables represents a function, we need to understand the definition of a function. A function is a relation in which each input [tex]\(x\)[/tex] is associated with exactly one output [tex]\(y\)[/tex]. In other words, no [tex]\(x\)[/tex]-value can correspond to more than one [tex]\(y\)[/tex]-value within the same table.
Let’s analyze each table:
Table W:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
-1 & 15 \\
\hline
-2 & 6 \\
\hline
0 & 15 \\
\hline
4 & 6 \\
\hline
\end{tabular}
\][/tex]
In table W, all x-values [tex]\((-1, -2, 0, 4)\)[/tex] are unique, and each x-value corresponds to exactly one y-value. Hence, Table W is a function.
Table X:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
0 & 4 \\
\hline
6 & 15 \\
\hline
0 & 6 \\
\hline
-2 & -1 \\
\hline
\end{tabular}
\][/tex]
In table X, the x-value 0 is repeated with different y-values (4 and 6). This means x-value 0 does not correspond to exactly one y-value. Hence, Table X is not a function.
Table Y:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
4 & 0 \\
\hline
-1 & -2 \\
\hline
6 & -2 \\
\hline
6 & 15 \\
\hline
\end{tabular}
\][/tex]
In table Y, the x-value 6 is repeated with different y-values (-2 and 15). This means x-value 6 does not correspond to exactly one y-value. Hence, Table Y is not a function.
Table Z:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
6 & -2 \\
\hline
4 & 0 \\
\hline
15 & - \\
\hline
4 & 3 \\
\hline
\end{tabular}
\][/tex]
In table Z, the x-value 4 is repeated with different y-values (0 and 3). This means x-value 4 does not correspond to exactly one y-value. Hence, Table Z is not a function.
Therefore, the only table that represents a function is:
Answer: A. W
