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Fill in the [tex]$y$[/tex] values of the [tex]$t$[/tex]-table for the function [tex]$y=\sqrt[3]{x}$[/tex].

[tex]\[
\begin{tabular}{c|c}
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-8 & \\
-1 & \\
0 & \\
1 & \\
8 & \\
\hline
\end{tabular}
\][/tex]

This is the graph of the function [tex]$y=\sqrt[3]{x}$[/tex].



Answer :

GinnyAnswer
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].

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