To determine which table shows a function that is decreasing only over the interval [tex]\((-1, 1)\)[/tex], we'll analyze each table row by row. We need to focus on the values of [tex]\(f(x)\)[/tex] within the interval [tex]\(-1 < x < 1\)[/tex], specifically looking at how these values change.
### Table 1
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & 0 \\
-1 & 3 \\
0 & 0 \\
1 & -3 \\
2 & 0 \\
\hline
\end{array}
\][/tex]
For [tex]\(x\)[/tex] in [tex]\((-1, 1)\)[/tex], the function's values are:
- [tex]\(f(-1)=3\)[/tex]
- [tex]\(f(0)=0\)[/tex]
- [tex]\(f(1)=-3\)[/tex]
Here, [tex]\(3 \rightarrow 0 \rightarrow -3\)[/tex] which is decreasing.
### Table 2
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & 10 \\
-1 & 8 \\
0 & 0 \\
1 & -8 \\
2 & -10 \\
\hline
\end{array}
\][/tex]
For [tex]\(x\)[/tex] in [tex]\((-1, 1)\)[/tex], the function's values are:
- [tex]\(f(-1)=8\)[/tex]
- [tex]\(f(0)=0\)[/tex]
- [tex]\(f(1)=-8\)[/tex]
Here, [tex]\(8 \rightarrow 0 \rightarrow -8\)[/tex] which is decreasing.
### Table 3
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & 0 \\
-1 & -3 \\
0 & 0 \\
1 & 3 \\
2 & 0 \\
\hline
\end{array}
\][/tex]
For [tex]\(x\)[/tex] in [tex]\((-1, 1)\)[/tex], the function's values are:
- [tex]\(f(-1)=-3\)[/tex]
- [tex]\(f(0)=0\)[/tex]
- [tex]\(f(1)=3\)[/tex]
Here, [tex]\(-3 \rightarrow 0 \rightarrow 3\)[/tex] which is increasing.
### Table 4
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & -10 \\
-1 & -8 \\
0 & 0 \\
1 & 8 \\
2 & 10 \\
\hline
\end{array}
\][/tex]
For [tex]\(x\)[/tex] in [tex]\((-1, 1)\)[/tex], the function's values are:
- [tex]\(f(-1)=-8\)[/tex]
- [tex]\(f(0)=0\)[/tex]
- [tex]\(f(1)=8\)[/tex]
Here, [tex]\(-8 \rightarrow 0 \rightarrow 8\)[/tex] which is increasing.
### Conclusion
By analyzing each table, we conclude that the functions in both Table 1 and Table 2 are decreasing over the interval [tex]\((-1, 1)\)[/tex]. Therefore, the correct tables are:
[tex]\[
\boxed{1 \text{ and } 2}
\][/tex]
