Answer
Compared with the graph of $f\left( x \right)=\frac{1}{x}$ , the graph of $g\left( x \right)=\frac{1}{x+2}-1$ is shifted 2 units left and 1 unit down.
Work Step by Step
On making the comparison of $f\left( x \right)=\frac{1}{x}$ with the graph of $g\left( x \right)=\frac{1}{x+2}-1$ , it can be observed that the graph of the later is obtained by shifting the graph of the former by 2 units left and 1 unit down.