Question

To graph the square root function y=13x−3−−−−√+2 , complete the table of data points for the function.(2 points) x y 3 4 7

Answer 1

To complete the table of data points for the function \( y = \sqrt{13x - 3} + 2 \), we will calculate the values of \( y \) for the given values of \( x \): 3, 4, and 7.

1. **For \( x = 3 \)**:
\[
y = \sqrt{13(3) - 3} + 2 = \sqrt{39 - 3} + 2 = \sqrt{36} + 2 = 6 + 2 = 8
\]
So, the point is \( (3, 8) \).

2. **For \( x = 4 \)**:
\[
y = \sqrt{13(4) - 3} + 2 = \sqrt{52 - 3} + 2 = \sqrt{49} + 2 = 7 + 2 = 9
\]
So, the point is \( (4, 9) \).

3. **For \( x = 7 \)**:
\[
y = \sqrt{13(7) - 3} + 2 = \sqrt{91 - 3} + 2 = \sqrt{88} + 2 \approx 9.38 + 2 = 11.38
\]
So, the point is \( (7, \sqrt{88} + 2) \approx (7, 11.38) \).

Now we can summarize the points:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
3 & 8 \\
4 & 9 \\
7 & 11.38 \\
\hline
\end{array}
\]

So, the completed table of data points is:
- \( (3, 8) \)
- \( (4, 9) \)
- \( (7, 11.38) \)