Complete the data table for the function
[tex]f(x)=\sqrt{x+2}-6[/tex].

\begin{tabular}{c|cccc}
[tex]$X$[/tex] & -2 & -1 & 2 & 7 \\
\hline
[tex]$Y$[/tex] & {[?]} & {[]} & {[]} & {[]}
\end{tabular}



Answer :

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]