To complete the table of data points for the function \( y = \sqrt[3]{13x - 3} + 2 \), we can calculate the values of \( y \) for each given \( x \) value:
Given Function
\[ y = \sqrt[3]{13x - 3} + 2 \]
x = 2
\[ y = \sqrt[3]{13(2) - 3} + 2 \ y = \sqrt[3]{26 - 3} + 2 \ y = \sqrt[3]{23} + 2 \ y \approx 2.843 + 2 \approx 4.843 \]
x = 3
\[ y = \sqrt[3]{13(3) - 3} + 2 \ y = \sqrt[3]{39 - 3} + 2 \ y = \sqrt[3]{36} + 2 \ y \approx 3.301 + 2 \approx 5.301 \]
x = 4
\[ y = \sqrt[3]{13(4) - 3} + 2 \ y = \sqrt[3]{52 - 3} + 2 \ y = \sqrt[3]{49} + 2 \ y \approx 3.659 + 2 \approx 5.659 \]
Completed Table
Now, the completed data points for the table are:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 2 & \approx 4.843 \ 3 & \approx 5.301 \ 4 & \approx 5.659 \ \hline \end{array} \]
You can round the \( y \) values to a suitable decimal place as needed. If you need further assistance, let me know!
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