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In which of the relations represented by the tables below is the output a function of the input?

Select all correct answers.

[tex]\[
\begin{tabular}{c|cccc}
Input & 6 & 2 & 0 & 7 \\
\hline
Output & 7 & -5 & 14 & 7 \\
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{c|cccc}
Input & -3 & 7 & 2 & 7 \\
\hline
Output & -1 & 4 & 12 & 13 \\
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{c|cccc}
Input & 0 & 9 & 0 & 2 \\
\hline
Output & -2 & 4 & 3 & 1 \\
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{c|cccc}
Input & 2 & -2 & 1 & 2 \\
\hline
Output & 11 & 14 & 8 & 12 \\
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{c|cccc}
Input & -2 & 6 & 0 & -3 \\
\hline
Output & 5 & 7 & 7 & 8 \\
\end{tabular}
\][/tex]

Sagot :

GinnyAnsweridn
Let's analyze each table to determine if the output is a function of the input.

1. First Table:

[tex]\[ \begin{tabular}{c|cccc} Input & 6 & 2 & 0 & 7 \\ \hline Output & 7 & -5 & 14 & 7 \end{tabular} \][/tex]

For this table, let's check the input-output pairs:

- (6, 7)
- (2, -5)
- (0, 14)
- (7, 7)

Each input has exactly one corresponding output:
- Input 6 maps to 7
- Input 2 maps to -5
- Input 0 maps to 14
- Input 7 maps to 7

Since no input is associated with more than one output, this table represents a function.

2. Second Table:

[tex]\[ \begin{tabular}{c|cccc} Input & -3 & 7 & 2 & 7 \\ \hline Output & -1 & 4 & 12 & 13 \end{tabular} \][/tex]

For this table, the pairs are:

- (-3, -1)
- (7, 4)
- (2, 12)
- (7, 13)

Here, the input 7 maps to two different outputs (4 and 13). Since one input maps to multiple outputs, this table does not represent a function.

3. Third Table:

[tex]\[ \begin{tabular}{c|cccc} Input & 0 & 9 & 0 & 2 \\ \hline Output & -2 & 4 & 3 & 1 \end{tabular} \][/tex]

For this table, the pairs are:

- (0, -2)
- (9, 4)
- (0, 3)
- (2, 1)

Here, the input 0 maps to two different outputs (-2 and 3). Since one input maps to multiple outputs, this table does not represent a function.

4. Fourth Table:

[tex]\[ \begin{tabular}{c|cccc} Input & 2 & -2 & 1 & 2 \\ \hline Output & 11 & 14 & 8 & 12 \end{tabular} \][/tex]

For this table, the pairs are:

- (2, 11)
- (-2, 14)
- (1, 8)
- (2, 12)

The input 2 maps to two different outputs (11 and 12). Since one input maps to multiple outputs, this table does not represent a function.

5. Fifth Table:

[tex]\[ \begin{tabular}{c|cccc} Input & -2 & 6 & 0 & -3 \\ \hline Output & 5 & 7 & 7 & 8 \end{tabular} \][/tex]

For this table, the pairs are:

- (-2, 5)
- (6, 7)
- (0, 7)
- (-3, 8)

Each input has exactly one corresponding output:
- Input -2 maps to 5
- Input 6 maps to 7
- Input 0 maps to 7
- Input -3 maps to 8

Since no input is associated with more than one output, this table represents a function.

Conclusion:

The tables that represent functions are the first and fifth tables.

Therefore, the correct answers are:
1. [tex]\(\begin{tabular}{c|cccc} Input & 6 & 2 & 0 & 7 \\ \hline Output & 7 & -5 & 14 & 7 \end{tabular}\)[/tex]
2. [tex]\(\begin{tabular}{c|cccc} Input & -2 & 6 & 0 & -3 \\ \hline Output & 5 & 7 & 7 & 8 \end{tabular}\)[/tex]
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