what is the equation of the horizontal asymptote of y = 1/(x + 2) - 2?

Explanation:

Step1: Recall horizontal - asymptote rule

For a rational function of the form $y=\frac{a}{x - h}+k$ (where $a\neq0$), the horizontal asymptote is $y = k$.

Step2: Identify $k$ in the given function

The given function is $y=\frac{1}{x + 2}-2$, which is in the form $y=\frac{a}{x - h}+k$ with $a = 1$, $h=-2$ and $k=-2$.

Answer:

$y=-2$