To complete the table for the function \( f(x) = \sqrt{x+3} + 4 \), let's evaluate the function at each given \( x \) value step-by-step.
1. For \( x = -3 \):
[tex]\[
f(-3) = \sqrt{-3 + 3} + 4 = \sqrt{0} + 4 = 0 + 4 = 4
\][/tex]
2. For \( x = -2 \):
[tex]\[
f(-2) = \sqrt{-2 + 3} + 4 = \sqrt{1} + 4 = 1 + 4 = 5
\][/tex]
3. For \( x = 1 \):
[tex]\[
f(1) = \sqrt{1 + 3} + 4 = \sqrt{4} + 4 = 2 + 4 = 6
\][/tex]
4. For \( x = 6 \):
[tex]\[
f(6) = \sqrt{6 + 3} + 4 = \sqrt{9} + 4 = 3 + 4 = 7
\][/tex]
Now, let's fill in the completed table with the calculated \( y \)-values.
[tex]\[
\begin{array}{r|r}
x & y \\
\hline
-3 & 4.0 \\
-2 & 5.0 \\
1 & 6.0 \\
6 & 7.0 \\
\end{array}
\][/tex]
