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Sagot :
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]
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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