To find the [tex]\( y \)[/tex]-values corresponding to each [tex]\( x \)[/tex]-value for the function [tex]\( y = x^4 \)[/tex], let us evaluate [tex]\( x^4 \)[/tex] for each given value of [tex]\( x \)[/tex].
Given [tex]\( x = -3 \)[/tex]:
[tex]\[ y = (-3)^4 = 81 \][/tex]
Given [tex]\( x = -1 \)[/tex]:
[tex]\[ y = (-1)^4 = 1 \][/tex]
Given [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 1^4 = 1 \][/tex]
Given [tex]\( x = -1 \)[/tex] again:
[tex]\[ y = (-1)^4 = 1 \][/tex]
Now, let's compile these results into the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
-3 & 81 \\
\hline
-1 & 1 \\
\hline
1 & 1 \\
\hline
-1 & 1 \\
\hline
\end{tabular}
\][/tex]
Therefore, this is the correct tabulated form of the function [tex]\( y = x^4 \)[/tex] for the given [tex]\( x \)[/tex]-values.
