To complete the table for the function \( y = \sqrt[3]{5x + 2} - 4 \), we will calculate \( y \) for each value of \( x \) provided in the table: \( -1 \), \( -2 \), and \( -3 \).
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For \( x = -1 \): \[ y = \sqrt[3]{5(-1) + 2} - 4 = \sqrt[3]{-5 + 2} - 4 = \sqrt[3]{-3} - 4 \approx -1.442 - 4 \approx -5.442 \]
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For \( x = -2 \): \[ y = \sqrt[3]{5(-2) + 2} - 4 = \sqrt[3]{-10 + 2} - 4 = \sqrt[3]{-8} - 4 = -2 - 4 = -6 \]
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For \( x = -3 \): \[ y = \sqrt[3]{5(-3) + 2} - 4 = \sqrt[3]{-15 + 2} - 4 = \sqrt[3]{-13} - 4 \approx -2.351 - 4 \approx -6.351 \]
Now, we can summarize the data points in the table:
\[ \begin{array}{|c|c|} \hline x & y \ \hline -1 & \approx -5.442 \ -2 & -6 \ -3 & \approx -6.351 \ \hline \end{array} \]
So, the completed table of data points is:
| \( x \) | \( y \) | |---------|----------------| | -1 | \(-5.442\) | | -2 | \(-6\) | | -3 | \(-6.351\) |