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
Remaining Attempts : 3

Answer 1

To complete the table of data points for the function \( y = \sqrt{13x - 3} + 2 \), we will substitute the values of \( x \) into the equation and compute the corresponding \( y \) values.

### For \( x = 3 \):
\[
y = \sqrt{13(3) - 3} + 2
\]
\[
y = \sqrt{39 - 3} + 2
\]
\[
y = \sqrt{36} + 2
\]
\[
y = 6 + 2 = 8
\]

### For \( x = 4 \):
\[
y = \sqrt{13(4) - 3} + 2
\]
\[
y = \sqrt{52 - 3} + 2
\]
\[
y = \sqrt{49} + 2
\]
\[
y = 7 + 2 = 9
\]

### For \( x = 7 \):
\[
y = \sqrt{13(7) - 3} + 2
\]
\[
y = \sqrt{91 - 3} + 2
\]
\[
y = \sqrt{88} + 2
\]
Calculating \( \sqrt{88} \):
\[
\sqrt{88} \approx 9.38 \, \text{(exactly } 2\sqrt{22} \text{)}
\]
\[
y \approx 9.38 + 2 \approx 11.38
\]

### Completed Table of Data Points
Now we can fill in the values in the table:

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

So the completed table is:

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