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
