To determine whether the output is a function of the input in each table, we need to check if each input uniquely corresponds to exactly one output. This means that for each input value, there should be only one associated output value. If any input value corresponds to more than one output value, the relation is not a function.
Let's examine each table:
Table 1:
[tex]\[
\begin{array}{c|cccc}
\text{Input} & -2 & 6 & 8 & -1 \\
\hline
\text{Output} & 10 & 12 & 10 & -2 \\
\end{array}
\][/tex]
In this table, all input values are unique: -2, 6, 8, and -1 each correspond to one unique output. Therefore, this relation is a function.
Table 2:
[tex]\[
\begin{array}{c|cccc}
\text{Input} & -5 & 4 & 4 & 2 \\
\hline
\text{Output} & -3 & 4 & 1 & -1 \\
\end{array}
\][/tex]
In this table, the input value 4 corresponds to two different outputs: 4 and 1. Therefore, this relation is not a function.
Table 3:
[tex]\[
\begin{array}{c|cccc}
\text{Input} & 3 & 7 & 0 & 4 \\
\hline
\text{Output} & 11 & 6 & 11 & 3 \\
\end{array}
\][/tex]
In this table, all input values are unique: 3, 7, 0, and 4 each correspond to one unique output. Therefore, this relation is a function.
Table 4:
[tex]\[
\begin{array}{c|cccc}
\text{Input} & 7 & 9 & 3 & 3 \\
\hline
\text{Output} & 11 & -1 & 5 & 1 \\
\end{array}
\][/tex]
In this table, the input value 3 corresponds to two different outputs: 5 and 1. Therefore, this relation is not a function.
Table 5:
[tex]\[
\begin{array}{c|cccc}
\text{Input} & 4 & -2 & 3 & 9 \\
\hline
\text{Output} & 12 & 7 & -5 & 12 \\
\end{array}
\][/tex]
In this table, all input values are unique: 4, -2, 3, and 9 each correspond to one unique output. Therefore, this relation is a function.
Conclusion:
The input-output pairs form functions in the following tables:
- Table 1
- Table 3
- Table 5
Therefore, the correct answers are:
- Table 1
- Table 3
- Table 5
