To graph the cube root function given by the equation \( y = 5\sqrt[3]{x} - 4 \), we will complete the table by calculating the value of \( y \) for each value of \( x \).
Given equation:
\[ y = 5\sqrt[3]{x} - 4 \]
Calculating values:
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For \( x = -1 \): \[ y = 5\sqrt[3]{-1} - 4 = 5(-1) - 4 = -5 - 4 = -9 \]
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For \( x = -2 \): \[ y = 5\sqrt[3]{-2} - 4 \approx 5(-1.2599) - 4 \approx -6.2995 - 4 \approx -10.2995 \approx -10.3 \text{ (rounded to one decimal)} \]
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For \( x = -3 \): \[ y = 5\sqrt[3]{-3} - 4 \approx 5(-1.442) - 4 \approx -7.21 - 4 \approx -11.21 \approx -11.2 \text{ (rounded to one decimal)} \]
Data Table:
\[ \begin{array}{|c|c|} \hline x & y \ \hline -1 & -9 \ -2 & -10.3 \ -3 & -11.2 \ \hline \end{array} \]
Final Table for Data Points:
- For \( x = -1 \), \( y = -9 \)
- For \( x = -2 \), \( y = -10.3 \)
- For \( x = -3 \), \( y = -11.2 \)
Feel free to ask if you need further calculations or information!