To complete the table for the function [tex]\( f(x) = \sqrt{x-5} + 3 \)[/tex], we will evaluate the function at each of the given [tex]\( x \)[/tex] values. Here are the detailed steps for each calculation:
1. For [tex]\( x = 5 \)[/tex]:
[tex]\[
f(5) = \sqrt{5 - 5} + 3 = \sqrt{0} + 3 = 0 + 3 = 3
\][/tex]
Therefore, when [tex]\( x = 5 \)[/tex], [tex]\( y = 3 \)[/tex].
2. For [tex]\( x = 6 \)[/tex]:
[tex]\[
f(6) = \sqrt{6 - 5} + 3 = \sqrt{1} + 3 = 1 + 3 = 4
\][/tex]
Therefore, when [tex]\( x = 6 \)[/tex], [tex]\( y = 4 \)[/tex].
3. For [tex]\( x = 9 \)[/tex]:
[tex]\[
f(9) = \sqrt{9 - 5} + 3 = \sqrt{4} + 3 = 2 + 3 = 5
\][/tex]
Therefore, when [tex]\( x = 9 \)[/tex], [tex]\( y = 5 \)[/tex].
4. For [tex]\( x = 14 \)[/tex]:
[tex]\[
f(14) = \sqrt{14 - 5} + 3 = \sqrt{9} + 3 = 3 + 3 = 6
\][/tex]
Therefore, when [tex]\( x = 14 \)[/tex], [tex]\( y = 6 \)[/tex].
After these calculations, the completed table is as follows:
[tex]\[
\begin{tabular}{c|c}
x & y \\
\hline
5 & 3 \\
6 & 4 \\
9 & 5 \\
14 & 6 \\
\end{tabular}
\][/tex]
So, the values are:
- When [tex]\( x = 5 \)[/tex], [tex]\( y = 3 \)[/tex].
- When [tex]\( x = 6 \)[/tex], [tex]\( y = 4 \)[/tex].
- When [tex]\( x = 9 \)[/tex], [tex]\( y = 5 \)[/tex].
- When [tex]\( x = 14 \)[/tex], [tex]\( y = 6 \)[/tex].
