To complete the table for the given square root function \( y = \frac{1}{3} \sqrt{x - 3} + 2 \), we will substitute the values of \( x \) into the equation to find corresponding values of \( y \).
Calculate \( y \) for each \( x \):
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For \( x = 3 \): \[ y = \frac{1}{3} \sqrt{3 - 3} + 2 = \frac{1}{3} \sqrt{0} + 2 = 0 + 2 = 2 \]
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For \( x = 4 \): \[ y = \frac{1}{3} \sqrt{4 - 3} + 2 = \frac{1}{3} \sqrt{1} + 2 = \frac{1}{3} \cdot 1 + 2 = \frac{1}{3} + 2 = \frac{1}{3} + \frac{6}{3} = \frac{7}{3} \approx 2.33 \]
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For \( x = 7 \): \[ y = \frac{1}{3} \sqrt{7 - 3} + 2 = \frac{1}{3} \sqrt{4} + 2 = \frac{1}{3} \cdot 2 + 2 = \frac{2}{3} + 2 = \frac{2}{3} + \frac{6}{3} = \frac{8}{3} \approx 2.67 \]
Complete the table with the calculated values:
| \( x \) | \( y \) | |---------|-------------| | 3 | 2 | | 4 | \(\frac{7}{3} \approx 2.33\) | | 7 | \(\frac{8}{3} \approx 2.67\) |
So the completed data points are:
- For \( x = 3, y = 2 \)
- For \( x = 4, y \approx 2.33 \)
- For \( x = 7, y \approx 2.67 \)