Question

To graph the square root function y=1/3x−3−−−−√+2 , complete the table of data points for the function.(2 points) x y 3 4 7

Answer 1

To graph the square root function \( y = \frac{1}{3}\sqrt{x - 3} + 2 \), we need to calculate the corresponding \( y \) values for the given \( x \) values: 3, 4, and 7.

### Step-by-Step Calculation:

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 \( (4, \frac{7}{3}) \) or approximately \( (4, 2.33) \).

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 \( (7, \frac{8}{3}) \) or approximately \( (7, 2.67) \).

### Completed Table:
| x | y |
|-----|-------|
| 3 | 2 |
| 4 | 2.33 |
| 7 | 2.67 |

Now you can use these points \( (3, 2) \), \( (4, 2.33) \), and \( (7, 2.67) \) to graph the function.