Answer
(see graph)
Work Step by Step
The computations below show some of the values of $x$ and $f(x)$ in the given equation, $
f(x)=\sqrt{x+2}-4
.$
If $x=-3,$ then
\begin{array}{l}\require{cancel}
f(x)=\sqrt{-3+2}-4
\\
f(x)=\sqrt{-1}-4
\\
f(x)=\text{not a real number}
\\\text{(*Note that the square root of negative numbers are imaginary numbers)}
.\end{array}
If $x=-2,$ then
\begin{array}{l}\require{cancel}
f(x)=\sqrt{-2+2}-4
\\
f(x)=\sqrt{0}-4
\\
f(x)=0-4
\\
f(x)=-4
.\end{array}
If $x=-1,$ then
\begin{array}{l}\require{cancel}
f(x)=\sqrt{-1+2}-4
\\
f(x)=\sqrt{1}-4
\\
f(x)=1-4
\\
f(x)=-3
.\end{array}
If $x=2,$ then
\begin{array}{l}\require{cancel}
f(x)=\sqrt{2+2}-4
\\
f(x)=\sqrt{4}-4
\\
f(x)=2-4
\\
f(x)=-2
.\end{array}
If $x=7,$ then
\begin{array}{l}\require{cancel}
f(x)=\sqrt{7+2}-4
\\
f(x)=\sqrt{9}-4
\\
f(x)=3-4
\\
f(x)=-1
.\end{array}
Summarizing the results above in the table of values below, the graph of the given function is shown.
