Answered

Question 3

Select all of the following tables which represent [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex].

\begin{tabular}{|r|r|}
\hline
[tex]\( x \)[/tex] & [tex]\( y \)[/tex] \\
\hline
-4 & 0 \\
\hline
1 & 2 \\
\hline
5 & 2 \\
\hline
9 & 8 \\
\hline
16 & 15 \\
\hline
\end{tabular}

\begin{tabular}{|r|r|}
\hline
[tex]\( x \)[/tex] & [tex]\( y \)[/tex] \\
\hline
-5 & -4 \\
\hline
3 & 1 \\
\hline
5 & 6 \\
\hline
8 & 9 \\
\hline
16 & 10 \\
\hline
\end{tabular}

\begin{tabular}{|r|r|}
\hline
[tex]\( x \)[/tex] & [tex]\( y \)[/tex] \\
\hline
-4 & -1 \\
\hline
3 & 1 \\
\hline
3 & 4 \\
\hline
8 & 9 \\
\hline
13 & 11 \\
\hline
\end{tabular}

\begin{tabular}{|r|r|}
\hline
[tex]\( x \)[/tex] & [tex]\( y \)[/tex] \\
\hline
-3 & -1 \\
\hline
1 & 2 \\
\hline
6 & 5 \\
\hline
8 & 7 \\
\hline
1 & 14 \\
\hline
\end{tabular}



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