To graph the function \( y = \sqrt{13x - 3} + 2 \), we will substitute the values of \( x \) into the function to find the corresponding \( y \) values for \( x = 3, 4, \) and \( 7 \).
For \( x = 3 \):
\[ y = \sqrt{13(3) - 3} + 2 \] \[ y = \sqrt{39 - 3} + 2 \] \[ y = \sqrt{36} + 2 \] \[ y = 6 + 2 = 8 \] So, when \( x = 3 \), \( y = 8 \).
For \( x = 4 \):
\[ y = \sqrt{13(4) - 3} + 2 \] \[ y = \sqrt{52 - 3} + 2 \] \[ y = \sqrt{49} + 2 \] \[ y = 7 + 2 = 9 \] So, when \( x = 4 \), \( y = 9 \).
For \( x = 7 \):
\[ y = \sqrt{13(7) - 3} + 2 \] \[ y = \sqrt{91 - 3} + 2 \] \[ y = \sqrt{88} + 2 \] \[ y \approx 9.38 + 2 \approx 11.38 \] So, when \( x = 7 \), \( y \approx 11.38 \).
Completed Table:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 3 & 8 \ 4 & 9 \ 7 & \approx 11.38 \ \hline \end{array} \]