Answer :
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
