Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine whether each table represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex], we must verify if each input [tex]\( x \)[/tex] corresponds to exactly one output [tex]\( y \)[/tex]. In other words, no [tex]\( x \)[/tex] value should repeat with different [tex]\( y \)[/tex] values.
### Table 1:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -4 & 0 \\ \hline 1 & 2 \\ \hline 5 & 2 \\ \hline 9 & 8 \\ \hline 16 & 15 \\ \hline \end{array} \][/tex]
- The [tex]\( x \)[/tex] values are: -4, 1, 5, 9, 16.
- Each [tex]\( x \)[/tex] value is unique.
This table represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 2:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -5 & -4 \\ \hline 3 & 1 \\ \hline 5 & 6 \\ \hline 8 & 9 \\ \hline 16 & 10 \\ \hline \end{array} \][/tex]
- The [tex]\( x \)[/tex] values are: -5, 3, 5, 8, 16.
- Each [tex]\( x \)[/tex] value is unique.
This table represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 3:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -4 & -1 \\ \hline 3 & 1 \\ \hline 3 & 4 \\ \hline 8 & 9 \\ \hline 13 & 11 \\ \hline \end{array} \][/tex]
- The [tex]\( x \)[/tex] values are: -4, 3, 3, 8, 13.
- The [tex]\( x \)[/tex] value 3 appears twice with different [tex]\( y \)[/tex] values (1 and 4).
This table does not represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 4:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -3 & -1 \\ \hline 1 & 2 \\ \hline 6 & 5 \\ \hline 8 & 7 \\ \hline 1 & 14 \\ \hline \end{array} \][/tex]
- The [tex]\( x \)[/tex] values are: -3, 1, 6, 8, 1.
- The [tex]\( x \)[/tex] value 1 appears twice with different [tex]\( y \)[/tex] values (2 and 14).
This table does not represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Conclusion
The tables that represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex] are:
- The first table
- The second table
### Table 1:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -4 & 0 \\ \hline 1 & 2 \\ \hline 5 & 2 \\ \hline 9 & 8 \\ \hline 16 & 15 \\ \hline \end{array} \][/tex]
- The [tex]\( x \)[/tex] values are: -4, 1, 5, 9, 16.
- Each [tex]\( x \)[/tex] value is unique.
This table represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 2:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -5 & -4 \\ \hline 3 & 1 \\ \hline 5 & 6 \\ \hline 8 & 9 \\ \hline 16 & 10 \\ \hline \end{array} \][/tex]
- The [tex]\( x \)[/tex] values are: -5, 3, 5, 8, 16.
- Each [tex]\( x \)[/tex] value is unique.
This table represents [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 3:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -4 & -1 \\ \hline 3 & 1 \\ \hline 3 & 4 \\ \hline 8 & 9 \\ \hline 13 & 11 \\ \hline \end{array} \][/tex]
- The [tex]\( x \)[/tex] values are: -4, 3, 3, 8, 13.
- The [tex]\( x \)[/tex] value 3 appears twice with different [tex]\( y \)[/tex] values (1 and 4).
This table does not represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Table 4:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -3 & -1 \\ \hline 1 & 2 \\ \hline 6 & 5 \\ \hline 8 & 7 \\ \hline 1 & 14 \\ \hline \end{array} \][/tex]
- The [tex]\( x \)[/tex] values are: -3, 1, 6, 8, 1.
- The [tex]\( x \)[/tex] value 1 appears twice with different [tex]\( y \)[/tex] values (2 and 14).
This table does not represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].
### Conclusion
The tables that represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex] are:
- The first table
- The second table
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 service. We're always here to provide accurate and up-to-date answers to all your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.