Certainly! Let's complete the table step by step for the function [tex]\( y = \sqrt[3]{x} + 7 \)[/tex].
First, we need to find the cube root of each [tex]\( x \)[/tex] value and then add 7 to it:
1. For [tex]\( x = -8 \)[/tex]:
[tex]\[ y = \sqrt[3]{-8} + 7 \][/tex]
[tex]\[ y = -2 + 7 \][/tex]
[tex]\[ y = 5 \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = \sqrt[3]{-1} + 7 \][/tex]
[tex]\[ y = -1 + 7 \][/tex]
[tex]\[ y = 6 \][/tex]
3. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = \sqrt[3]{1} + 7 \][/tex]
[tex]\[ y = 1 + 7 \][/tex]
[tex]\[ y = 8 \][/tex]
4. For [tex]\( x = 8 \)[/tex]:
[tex]\[ y = \sqrt[3]{8} + 7 \][/tex]
[tex]\[ y = 2 + 7 \][/tex]
[tex]\[ y = 9 \][/tex]
So, after calculating the values of [tex]\( y \)[/tex], we get the following table:
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\hline
$x$ & -8 & -1 & 1 & 8 \\
\hline
$y$ & 5 & 6 & 8 & 9 \\
\hline
\end{tabular}
\][/tex]
Hence, the correct answer is:
B) [tex]\( 5, 6, 8, 9 \)[/tex]
