Answer
please see image
.
Work Step by Step
(Work done in online calculator desmos.com)
Let $f(x)=\displaystyle \frac{1}{x}$ (graph: blue, dashed)
$g(x)=\displaystyle \frac{1}{x+2}-2=f(x+2)-2$
So, the graph of $g$ (red, solid line)
is obtained by
1. shifting the graph of $f(x)=\displaystyle \frac{1}{x}$ to the left by $2$ units
(graph of $f(x+2)=\displaystyle \frac{1}{x+2}$, green, dashed)
and then
2. shifting the graph of $f(x+2)$ downward by 2 units.
( $f(x+1)-2=g(x))$
(A shift to the left or right moves the vertical asymptote
A shift up or down moves the horizontal asymptote)
