To determine which tables represent constant functions, we need to analyze the [tex]\(y\)[/tex]-values for each table. A function is considered constant if the [tex]\(y\)[/tex]-values do not change regardless of the [tex]\(x\)[/tex]-values.
Table 1:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & -1 \\
\hline
2 & 0 \\
\hline
2 & 1 \\
\hline
\end{array}
\][/tex]
In this table, [tex]\(x\)[/tex] is always 2, but the [tex]\(y\)[/tex]-values are [tex]\(-1\)[/tex], [tex]\(0\)[/tex], and [tex]\(1\)[/tex]. Since the [tex]\(y\)[/tex]-values are different, this is not 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]
In this table, both the [tex]\(x\)[/tex]-values and [tex]\(y\)[/tex]-values change. The [tex]\(y\)[/tex]-values are [tex]\(-3\)[/tex], [tex]\(-7\)[/tex], and [tex]\(-11\)[/tex], which are not the same. Therefore, this is not a constant function.
Table 3:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & 3 \\
\hline
4 & 3 \\
\hline
\end{array}
\][/tex]
In this table, the [tex]\(y\)[/tex]-value remains [tex]\(3\)[/tex] regardless of the [tex]\(x\)[/tex]-value. Since all the [tex]\(y\)[/tex]-values are the same, this table represents a constant function.
Based on this analysis, the correct answer is:
Table 3 represents a constant function.
