Sure, let's complete the data table for the given function [tex]\( f(x) = \sqrt{x - 5} - 1 \)[/tex].
First, we need to compute [tex]\( f(x) \)[/tex] for each value of [tex]\( x \)[/tex] provided.
1. For [tex]\( x = 5 \)[/tex]:
[tex]\[
f(5) = \sqrt{5 - 5} - 1 = \sqrt{0} - 1 = 0 - 1 = -1
\][/tex]
So, [tex]\( f(5) = -1 \)[/tex].
2. For [tex]\( x = 6 \)[/tex]:
[tex]\[
f(6) = \sqrt{6 - 5} - 1 = \sqrt{1} - 1 = 1 - 1 = 0
\][/tex]
So, [tex]\( f(6) = 0 \)[/tex].
3. For [tex]\( x = 9 \)[/tex]:
[tex]\[
f(9) = \sqrt{9 - 5} - 1 = \sqrt{4} - 1 = 2 - 1 = 1
\][/tex]
So, [tex]\( f(9) = 1 \)[/tex].
4. For [tex]\( x = 14 \)[/tex]:
[tex]\[
f(14) = \sqrt{14 - 5} - 1 = \sqrt{9} - 1 = 3 - 1 = 2
\][/tex]
So, [tex]\( f(14) = 2 \)[/tex].
Now, we can complete the data table:
[tex]\[
\begin{array}{c|c|c|c|c}
X & 5 & 6 & 9 & 14 \\
\hline
Y & -1 & 0 & 1 & 2 \\
\end{array}
\][/tex]
