To determine which tables represent constant functions, we need to identify tables where the [tex]\( y \)[/tex]-values remain the same regardless of the [tex]\( x \)[/tex]-values.
Let's analyze each table provided:
Table 1:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & -1 \\
\hline
2 & 0 \\
\hline
2 & 1 \\
\hline
\end{array}
\][/tex]
Here, the [tex]\( y \)[/tex]-values are -1, 0, and 1. Since they are not the same, this table does not represent a constant function.
Table 2:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & -3 \\
\hline
4 & -7 \\
\hline
6 & -11 \\
\hline
\end{array}
\][/tex]
Here, the [tex]\( y \)[/tex]-values are -3, -7, and -11. Since they are not the same, this table does not represent a constant function.
Table 3:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & 3 \\
\hline
4 & 3 \\
\hline
6 & 3 \\
\hline
\end{array}
\][/tex]
Here, the [tex]\( y \)[/tex]-values are 3, 3, and 3. Since they are all the same, this table represents a constant function.
Table 4:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 3 \\
\hline
2 & 12 \\
\hline
3 & 27 \\
\hline
\end{array}
\][/tex]
Here, the [tex]\( y \)[/tex]-values are 3, 12, and 27. Since they are not the same, this table does not represent a constant function.
Table 5:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & -1 \\
\hline
2 & -1 \\
\hline
3 & -1 \\
\hline
\end{array}
\][/tex]
Here, the [tex]\( y \)[/tex]-values are -1, -1, and -1. Since they are all the same, this table represents a constant function.
Based on this analysis, the tables that represent constant functions are:
- Table 3: [tex]\(\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & 3 \\
\hline
4 & 3 \\
\hline
6 & 3 \\
\hline
\end{array}\)[/tex]
- Table 5: [tex]\(\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & -1 \\
\hline
2 & -1 \\
\hline
3 & -1 \\
\hline
\end{array}\)[/tex]
Thus, the correct answers are Tables 3 and 5.
