To find the values of [tex]\( y = f(x) \)[/tex] for the given values of [tex]\( x \)[/tex], we use the function [tex]\( f(x) = \sqrt{x - 5} + 3 \)[/tex].
Let's compute the value of [tex]\( y \)[/tex] for each given [tex]\( x \)[/tex]:
1. For [tex]\( x = 5 \)[/tex]:
[tex]\[
f(5) = \sqrt{5 - 5} + 3 = \sqrt{0} + 3 = 0 + 3 = 3
\][/tex]
So, [tex]\( y = 3 \)[/tex] when [tex]\( x = 5 \)[/tex].
2. For [tex]\( x = 6 \)[/tex]:
[tex]\[
f(6) = \sqrt{6 - 5} + 3 = \sqrt{1} + 3 = 1 + 3 = 4
\][/tex]
So, [tex]\( y = 4 \)[/tex] when [tex]\( x = 6 \)[/tex].
3. For [tex]\( x = 9 \)[/tex]:
[tex]\[
f(9) = \sqrt{9 - 5} + 3 = \sqrt{4} + 3 = 2 + 3 = 5
\][/tex]
So, [tex]\( y = 5 \)[/tex] when [tex]\( x = 9 \)[/tex].
4. For [tex]\( x = 14 \)[/tex]:
[tex]\[
f(14) = \sqrt{14 - 5} + 3 = \sqrt{9} + 3 = 3 + 3 = 6
\][/tex]
So, [tex]\( y = 6 \)[/tex] when [tex]\( x = 14 \)[/tex].
Putting these values into the table, we get:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
5 & 3 \\
6 & 4 \\
9 & 5 \\
14 & 6 \\
\end{array}
\][/tex]
