Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
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.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.