Which table represents a function?

\begin{tabular}{|l|c|c|c|c|c|}
\hline
Input (x) & -4 & -2 & -2 & -1 & 0 \\
\hline
Output (y) & 6 & 8 & 10 & 12 & 14 \\
\hline
\end{tabular}

\begin{tabular}{|l|c|c|c|c|c|}
\hline
Input (x) & -2 & 0 & 2 & 4 & 6 \\
\hline
Output (y) & 3 & 3 & 6 & 6 & 9 \\
\hline
\end{tabular}

\begin{tabular}{|l|c|c|c|c|c|}
\hline
Input (x) & 10 & 20 & 30 & 30 & 40 \\
\hline
Output (y) & -5 & -6 & -7 & -8 & -9 \\
\hline
\end{tabular}

\begin{tabular}{|l|c|c|c|c|c|}
\hline
Input (x) & -5 & -5 & -5 & -5 & -5 \\
\hline
Output (y) & -5 & 0 & 5 & 10 & 15 \\
\hline
\end{tabular}



Answer :

To determine which table represents a function, we need to ensure that for every unique input value [tex]\( x \)[/tex], there is only one corresponding output value [tex]\( y \)[/tex]. This means that each input value should map to exactly one output value.

Let's go through the tables one by one to check this property:

### Table 1
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Input (x)} & -4 & -2 & -2 & -1 & 0 \\ \hline \text{Output (y)} & 6 & 8 & 10 & 12 & 14 \\ \hline \end{array} \][/tex]

- The input value [tex]\(-2\)[/tex] appears twice, with different outputs ([tex]\(8\)[/tex] and [tex]\(10\)[/tex]).
- This violates the definition of a function.

Table 1 does NOT represent a function.

### Table 2
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Input (x)} & -2 & 0 & 2 & 4 & 6 \\ \hline \text{Output (y)} & 3 & 3 & 6 & 6 & 9 \\ \hline \end{array} \][/tex]

- Each input value [tex]\(-2, 0, 2, 4, 6\)[/tex] is unique and maps to one specific output value.
- There are no repeated input values.

Table 2 represents a function.

### Table 3
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Input (x)} & 10 & 20 & 30 & 30 & 40 \\ \hline \text{Output (y)} & -5 & -6 & -7 & -8 & -9 \\ \hline \end{array} \][/tex]

- The input value [tex]\(30\)[/tex] appears twice, with different outputs ([tex]\(-7\)[/tex] and [tex]\(-8\)[/tex]).
- This violates the definition of a function.

Table 3 does NOT represent a function.

### Table 4
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Input (x)} & -5 & -5 & -5 & -5 & -5 \\ \hline \text{Output (y)} & -5 & 0 & 5 & 10 & 15 \\ \hline \end{array} \][/tex]

- The input value [tex]\(-5\)[/tex] appears multiple times with different outputs ([tex]\(-5, 0, 5, 10, 15\)[/tex]).
- This violates the definition of a function.

Table 4 does NOT represent a function.

Conclusion:
Among the given tables, only Table 2 represents a function.