To fill in the table using the function [tex]\( f(x) = \sqrt{x - 5} \)[/tex], let's evaluate the function for each given value of [tex]\( x \)[/tex].
1. For [tex]\( x = -4 \)[/tex]:
[tex]\[
f(-4) = \sqrt{-4 - 5} = \sqrt{-9}
\][/tex]
Since the square root of a negative number is not a real number, we say:
[tex]\[
f(-4) = \text{Not a real number}
\][/tex]
2. For [tex]\( x = 5 \)[/tex]:
[tex]\[
f(5) = \sqrt{5 - 5} = \sqrt{0}
\][/tex]
Since the square root of 0 is 0, we have:
[tex]\[
f(5) = 0.0
\][/tex]
3. For [tex]\( x = 9 \)[/tex]:
[tex]\[
f(9) = \sqrt{9 - 5} = \sqrt{4}
\][/tex]
Since the square root of 4 is 2, we get:
[tex]\[
f(9) = 2.0
\][/tex]
Now we can fill in the table:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-4 & Not a real number \\
\hline
5 & 0.0 \\
\hline
9 & 2.0 \\
\hline
\end{tabular}
