Sure, let's complete the table of values.
You have the function [tex]\(4^{-x}\)[/tex] and the values of [tex]\(x\)[/tex]. Now we need to find the corresponding values of [tex]\(4^{-x}\)[/tex] for [tex]\(x = 0\)[/tex], [tex]\(x = 2\)[/tex], and [tex]\(x = 4\)[/tex].
Given the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $4^{-x}$ \\
\hline
-1 & 4 \\
\hline
0 & $a$ \\
\hline
2 & $b$ \\
\hline
4 & $c$ \\
\hline
\end{tabular}
\][/tex]
Now we find:
- When [tex]\(x = 0\)[/tex], [tex]\(4^{-0} = 1\)[/tex], so [tex]\(a = 1\)[/tex].
- When [tex]\(x = 2\)[/tex], [tex]\(4^{-2} = 0.0625\)[/tex], so [tex]\(b = 0.0625\)[/tex].
- When [tex]\(x = 4\)[/tex], [tex]\(4^{-4} = 0.00390625\)[/tex], so [tex]\(c = 0.00390625\)[/tex].
Therefore, the completed table and the values are:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $4^{-x}$ \\
\hline
-1 & 4 \\
\hline
0 & 1 \\
\hline
2 & 0.0625 \\
\hline
4 & 0.00390625 \\
\hline
\end{tabular}
\][/tex]
[tex]\[
\begin{array}{l}
a = 1, \quad b = 0.0625, \quad c = 0.00390625
\end{array}
\][/tex]
