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Sagot :
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]
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]
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