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Sagot :
To determine which of the given tables represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex], we need to check if for each table, each [tex]\( x \)[/tex] value corresponds to exactly one [tex]\( y \)[/tex] value.
Let's analyze each table one by one:
### Table 1:
[tex]\[ \begin{tabular}{|l|l|l|l|} \hline$x$ & 2 & 8 & 11 \\ \hline$y$ & 5 & 9 & 14 \\ \hline \end{tabular} \][/tex]
For [tex]\( x = 2 \)[/tex], [tex]\( y = 5 \)[/tex].
For [tex]\( x = 8 \)[/tex], [tex]\( y = 9 \)[/tex].
For [tex]\( x = 11 \)[/tex], [tex]\( y = 14 \)[/tex].
Each [tex]\( x \)[/tex] value corresponds to exactly one [tex]\( y \)[/tex] value. Therefore, this table represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 2:
[tex]\[ \begin{tabular}{|r|r|r|r|} \hline$x$ & 2 & 8 & 11 \\ \hline$y$ & 5 & 9 & 9 \\ \hline \end{tabular} \][/tex]
For [tex]\( x = 2 \)[/tex], [tex]\( y = 5 \)[/tex].
For [tex]\( x = 8 \)[/tex], [tex]\( y = 9 \)[/tex].
For [tex]\( x = 11 \)[/tex], [tex]\( y = 9 \)[/tex].
Each [tex]\( x \)[/tex] value corresponds to exactly one [tex]\( y \)[/tex] value. Therefore, this table represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 3:
[tex]\[ \begin{tabular}{|r|r|r|r|} \hline$x$ & 2 & 8 & 8 \\ \hline$y$ & 5 & 9 & 14 \\ \hline \end{tabular} \][/tex]
For [tex]\( x = 2 \)[/tex], [tex]\( y = 5 \)[/tex].
For [tex]\( x = 8 \)[/tex], [tex]\( y = 9 \)[/tex] and [tex]\( y = 14 \)[/tex].
Here, we have one [tex]\( x \)[/tex] value (8) corresponding to two different [tex]\( y \)[/tex] values (9 and 14). This violates the definition of a function, which states that each [tex]\( x \)[/tex] must map to exactly one [tex]\( y \)[/tex]. Therefore, this table does not represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Conclusion:
- The first table and the second table both represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
- The third table does not represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
Hence, the correct tables are the first and the second.
Let's analyze each table one by one:
### Table 1:
[tex]\[ \begin{tabular}{|l|l|l|l|} \hline$x$ & 2 & 8 & 11 \\ \hline$y$ & 5 & 9 & 14 \\ \hline \end{tabular} \][/tex]
For [tex]\( x = 2 \)[/tex], [tex]\( y = 5 \)[/tex].
For [tex]\( x = 8 \)[/tex], [tex]\( y = 9 \)[/tex].
For [tex]\( x = 11 \)[/tex], [tex]\( y = 14 \)[/tex].
Each [tex]\( x \)[/tex] value corresponds to exactly one [tex]\( y \)[/tex] value. Therefore, this table represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 2:
[tex]\[ \begin{tabular}{|r|r|r|r|} \hline$x$ & 2 & 8 & 11 \\ \hline$y$ & 5 & 9 & 9 \\ \hline \end{tabular} \][/tex]
For [tex]\( x = 2 \)[/tex], [tex]\( y = 5 \)[/tex].
For [tex]\( x = 8 \)[/tex], [tex]\( y = 9 \)[/tex].
For [tex]\( x = 11 \)[/tex], [tex]\( y = 9 \)[/tex].
Each [tex]\( x \)[/tex] value corresponds to exactly one [tex]\( y \)[/tex] value. Therefore, this table represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 3:
[tex]\[ \begin{tabular}{|r|r|r|r|} \hline$x$ & 2 & 8 & 8 \\ \hline$y$ & 5 & 9 & 14 \\ \hline \end{tabular} \][/tex]
For [tex]\( x = 2 \)[/tex], [tex]\( y = 5 \)[/tex].
For [tex]\( x = 8 \)[/tex], [tex]\( y = 9 \)[/tex] and [tex]\( y = 14 \)[/tex].
Here, we have one [tex]\( x \)[/tex] value (8) corresponding to two different [tex]\( y \)[/tex] values (9 and 14). This violates the definition of a function, which states that each [tex]\( x \)[/tex] must map to exactly one [tex]\( y \)[/tex]. Therefore, this table does not represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Conclusion:
- The first table and the second table both represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
- The third table does not represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
Hence, the correct tables are the first and the second.
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