Sure, let's complete the data table for the function \( f(x) = \sqrt{x+2} - 6 \).
Given:
[tex]\[
f(x) = \sqrt{x+2} - 6
\][/tex]
We need to find the values of \( f(x) \) for \( x = -2, -1, 2, 7 \).
1. For \( x = -2 \):
[tex]\[
f(-2) = \sqrt{-2 + 2} - 6 = \sqrt{0} - 6 = 0 - 6 = -6
\][/tex]
2. For \( x = -1 \):
[tex]\[
f(-1) = \sqrt{-1 + 2} - 6 = \sqrt{1} - 6 = 1 - 6 = -5
\][/tex]
3. For \( x = 2 \):
[tex]\[
f(2) = \sqrt{2 + 2} - 6 = \sqrt{4} - 6 = 2 - 6 = -4
\][/tex]
4. For \( x = 7 \):
[tex]\[
f(7) = \sqrt{7 + 2} - 6 = \sqrt{9} - 6 = 3 - 6 = -3
\][/tex]
Now, we can complete the data table:
[tex]\[
\begin{tabular}{c|cccc}
X & -2 & -1 & 2 & 7 \\
\hline
Y & -6 & -5 & -4 & -3 \\
\end{tabular}
\][/tex]
So, the completed data table looks like this:
[tex]\[
\begin{tabular}{c|cccc}
X & -2 & -1 & 2 & 7 \\
\hline
Y & -6 & -5 & -4 & -3 \\
\end{tabular}
\][/tex]
