To graph the cube root function given by the equation \( y = 5\sqrt[3]{x} + 2 - 3 - 4 \), we first simplify this expression. The function simplifies as follows:
\( y = 5\sqrt[3]{x} - 5 \)
Now, we will calculate the value of \( y \) for the specified \( x \) values (-1, -2, and -3):
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For \( x = -1 \): \[ y = 5\sqrt[3]{-1} - 5 \] \(\sqrt[3]{-1} = -1\), so: \[ y = 5(-1) - 5 = -5 - 5 = -10 \]
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For \( x = -2 \): \[ y = 5\sqrt[3]{-2} - 5 \] To find \(\sqrt[3]{-2}\), we calculate: \(\sqrt[3]{-2} \approx -1.26\), so: \[ y = 5(-1.26) - 5 \approx -6.3 - 5 \approx -11.3 \]
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For \( x = -3 \): \[ y = 5\sqrt[3]{-3} - 5 \] To find \(\sqrt[3]{-3}\), we calculate: \(\sqrt[3]{-3} \approx -1.442\), so: \[ y = 5(-1.442) - 5 \approx -7.21 - 5 = -12.21 \]
Now, we can complete the table of data points:
\[ \begin{array}{|c|c|} \hline x & y \ \hline -1 & -10 \ -2 & -11.3 \ -3 & -12.21 \ \hline \end{array} \]