Answer
The graph has a vertical asymptote at $x=-2$. The graph intersects the x-axis at $\left( \frac{-3}{2},0 \right)$ and y-axis at $\left( 0,-\frac{3}{2} \right)$.
Work Step by Step
First, plot the graph for $f\left( x \right)\ =\ \frac{1}{x}$:
Now, $f\left( x\ +\ a \right)$ implies that the graph is shifted leftwards by $a$ units.
Plot $y\ =\ \frac{1}{x\ +\ 2}$ by shifting the graph of $f\left( x \right)\ =\ \frac{1}{x}$ , $2$ units to the left.
Again, $f\left( x \right)\ -\ a$ implies a downwards shift in the graph by $a$ units.
Plot $g\left( x \right)\ =\ \frac{1}{x\ +\ 2}\ -\ 2$ by shifting the graph of $y\ =\ \frac{1}{x\ +\ 2}$ , $2$ units downwards.
