To graph the given function [tex]\( f(x) = 2^x \)[/tex], we need to calculate the values of [tex]\( f(x) \)[/tex] for the specified [tex]\( x \)[/tex]-values. Let's fill in the table of coordinates.
Given [tex]\( f(x) = 2^x \)[/tex]:
1. When [tex]\( x = -2 \)[/tex]:
[tex]\[
f(-2) = 2^{-2} = \frac{1}{2^2} = \frac{1}{4}
\][/tex]
2. When [tex]\( x = -1 \)[/tex]:
[tex]\[
f(-1) = 2^{-1} = \frac{1}{2^1} = \frac{1}{2}
\][/tex]
3. When [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 2^0 = 1
\][/tex]
4. When [tex]\( x = 1 \)[/tex]:
[tex]\[
f(1) = 2^1 = 2
\][/tex]
5. When [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 2^2 = 4
\][/tex]
Now, let's complete the table with these values:
\begin{tabular}{|c|c|c|c|c|c|}
\hline [tex]$x$[/tex] & -2 & -1 & 0 & 1 & 2 \\
\hline [tex]$y$[/tex] & [tex]\(\frac{1}{4}\)[/tex] & [tex]\(\frac{1}{2}\)[/tex] & 1 & 2 & 4 \\
\hline
\end{tabular}
