To fill in the \( y \) values for the function \( y = \sqrt[3]{x} \) in the \( t \)-table, we compute each \( y \) value corresponding to each given \( x \) value:
1. For \( x = -8 \):
[tex]\[
y = \sqrt[3]{-8} = (1.0000000000000002+1.7320508075688772j)
\][/tex]
2. For \( x = -1 \):
[tex]\[
y = \sqrt[3]{-1} = (0.5000000000000001+0.8660254037844386j)
\][/tex]
3. For \( x = 0 \):
[tex]\[
y = \sqrt[3]{0} = 0.0
\][/tex]
4. For \( x = 1 \):
[tex]\[
y = \sqrt[3]{1} = 1.0
\][/tex]
5. For \( x = 8 \):
[tex]\[
y = \sqrt[3]{8} = 2.0
\][/tex]
Now, we can fill in the \( t \)-table as follows:
[tex]\[
\begin{tabular}{c|c|}
x & y \\
\hline
-8 & (1.0000000000000002+1.7320508075688772j) \\
-1 & (0.5000000000000001+0.8660254037844386j) \\
0 & 0.0 \\
1 & 1.0 \\
8 & 2.0 \\
\hline
\end{tabular}
\][/tex]
Thus, the [tex]\( t \)[/tex]-table is completed with the respective [tex]\( y \)[/tex] values for the function [tex]\( y = \sqrt[3]{x} \)[/tex].
