Question

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

Answer 1

To complete the table for the function \( y = \frac{1}{3} \sqrt{x - 3} + 2 \), we'll compute the values of \( y \) for the given \( x \) values: \( x = 3, 4, 7 \).

### Step-by-step calculations:

1. **For \( x = 3 \)**:
\[
y = \frac{1}{3} \sqrt{3 - 3} + 2 = \frac{1}{3} \sqrt{0} + 2 = 0 + 2 = 2
\]
So, when \( x = 3 \), \( y = 2 \).

2. **For \( x = 4 \)**:
\[
y = \frac{1}{3} \sqrt{4 - 3} + 2 = \frac{1}{3} \sqrt{1} + 2 = \frac{1}{3} \cdot 1 + 2 = \frac{1}{3} + 2 = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3}
\]
So, when \( x = 4 \), \( y = \frac{7}{3} \).

3. **For \( x = 7 \)**:
\[
y = \frac{1}{3} \sqrt{7 - 3} + 2 = \frac{1}{3} \sqrt{4} + 2 = \frac{1}{3} \cdot 2 + 2 = \frac{2}{3} + 2 = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}
\]
So, when \( x = 7 \), \( y = \frac{8}{3} \).

### Summary of Data Points:
- For \( x = 3 \), \( y = 2 \)
- For \( x = 4 \), \( y = \frac{7}{3} \)
- For \( x = 7 \), \( y = \frac{8}{3} \)

### Completed Table:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
3 & 2 \\
4 & \frac{7}{3} \\
7 & \frac{8}{3} \\
\hline
\end{array}
\]