Question

To graph the square root function y = 1/3 * sqrt(x - 3) + 2 complete the table of data points for the function (2 points)

Answer 1

To complete the table of data points for the function \( y = \frac{1}{3} \sqrt{x - 3} + 2 \), we need to select some values for \( x \) that are greater than or equal to 3, since the square root function is only defined for \( x \geq 3 \). Here are a few values we can use:

1. **When \( x = 3 \)**:
\[
y = \frac{1}{3} \sqrt{3 - 3} + 2 = \frac{1}{3} \sqrt{0} + 2 = 0 + 2 = 2
\]
So, the point is \( (3, 2) \).

2. **When \( x = 4 \)**:
\[
y = \frac{1}{3} \sqrt{4 - 3} + 2 = \frac{1}{3} \sqrt{1} + 2 = \frac{1}{3} + 2 = \frac{1}{3} + \frac{6}{3} = \frac{7}{3} \approx 2.33
\]
So, the point is \( (4, \frac{7}{3}) \).

3. **When \( x = 7 \)**:
\[
y = \frac{1}{3} \sqrt{7 - 3} + 2 = \frac{1}{3} \sqrt{4} + 2 = \frac{1}{3} \cdot 2 + 2 = \frac{2}{3} + 2 = \frac{2}{3} + \frac{6}{3} = \frac{8}{3} \approx 2.67
\]
So, the point is \( (7, \frac{8}{3}) \).

4. **When \( x = 10 \)**:
\[
y = \frac{1}{3} \sqrt{10 - 3} + 2 = \frac{1}{3} \sqrt{7} + 2 \approx \frac{1}{3} \cdot 2.64575 + 2 \approx 0.882 + 2 \approx 2.88
\]
So, the point is \( (10, 2.88) \).

Based on these calculations, we can compile the data points as follows:

| \( x \) | \( y \) |
|---------|-----------------------|
| 3 | 2 |
| 4 | \(\frac{7}{3} \approx 2.33\) |
| 7 | \(\frac{8}{3} \approx 2.67\) |
| 10 | \(\approx 2.88\) |

Feel free to add more points or use different values of \( x \) if you wish to examine the function more thoroughly!