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Complete the table of values for the function:

[tex]\[
f(x) = \left(\frac{1}{3}\right)^x
\][/tex]

[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & a \\
\hline
-1 & b \\
\hline
0 & c \\
\hline
1 & \frac{1}{3} \\
\hline
2 & \frac{1}{9} \\
\hline
\end{array}
\][/tex]

[tex]\[
a = \square
\][/tex]

[tex]\[
b = \square
\][/tex]

[tex]\[
c = \square
\][/tex]

Sagot :

GinnyAnswer
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]
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