To complete the table of data points for the function \( y = \frac{1}{3}\sqrt{x} - 3 + 2 \), we will calculate the values of \( y \) for each given \( x \).
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For \( x = 3 \): \[ y = \frac{1}{3}\sqrt{3} - 3 + 2 \] \[ \sqrt{3} \approx 1.732 \] \[ y \approx \frac{1}{3}(1.732) - 3 + 2 = \frac{1.732}{3} - 3 + 2 \approx 0.577 - 3 + 2 \approx -0.423 \]
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For \( x = 4 \): \[ y = \frac{1}{3}\sqrt{4} - 3 + 2 \] \[ \sqrt{4} = 2 \] \[ y = \frac{1}{3}(2) - 3 + 2 = \frac{2}{3} - 3 + 2 = \frac{2}{3} - 1 \approx -0.333 \]
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For \( x = 7 \): \[ y = \frac{1}{3}\sqrt{7} - 3 + 2 \] \[ \sqrt{7} \approx 2.646 \] \[ y \approx \frac{1}{3}(2.646) - 3 + 2 = \frac{2.646}{3} - 3 + 2 \approx 0.882 - 3 + 2 \approx -0.118 \]
Here is the completed table:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 3 & -0.423 \ 4 & -0.333 \ 7 & -0.118 \ \hline \end{array} \]