Let's complete the table of values step-by-step.
We are given the function [tex]\( f(x) = \left( \frac{1}{3} \right)^x \)[/tex].
We need to find the values of [tex]\( f(x) \)[/tex] at different points [tex]\( x \)[/tex].
1. For [tex]\( x = -2 \)[/tex]:
[tex]\( f(-2) = \left( \frac{1}{3} \right)^{-2} = 9 \)[/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\( f(-1) = \left( \frac{1}{3} \right)^{-1} = 3 \)[/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\( f(0) = \left( \frac{1}{3} \right)^0 = 1 \)[/tex]
Given these values, we complete the table as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & 9 \\
\hline
-1 & 3 \\
\hline
0 & 1 \\
\hline
1 & \frac{1}{3} \\
\hline
2 & \frac{1}{9} \\
\hline
\end{array}
\][/tex]
