To complete the table, we need to find the value of the function [tex]\( f(x) = x^5 + (x + 3)^2 \)[/tex] at [tex]\( x = -1 \)[/tex].
1. Start by substituting [tex]\( x = -1 \)[/tex] into the function.
[tex]\[
f(-1) = (-1)^5 + (-1 + 3)^2
\][/tex]
2. Calculate [tex]\( (-1)^5 \)[/tex].
[tex]\[
(-1)^5 = -1
\][/tex]
3. Calculate [tex]\( (-1 + 3)^2 \)[/tex].
[tex]\[
-1 + 3 = 2
\][/tex]
[tex]\[
2^2 = 4
\][/tex]
4. Add the results from the previous steps.
[tex]\[
f(-1) = -1 + 4 = 3
\][/tex]
Therefore, the value of [tex]\( f(-1) \)[/tex] is 3.
This means the complete table is:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-2 & -31 \\
\hline
-1 & 3 \\
\hline
0 & 9 \\
\hline
1 & 17 \\
\hline
\end{tabular}
The value that completes the table is [tex]\( 3 \)[/tex].
