Answer
shift $\frac{1}{x^2}$ to the left units, reflect across the x-axis, then shift down 3 units,
(a) domain $(-\infty,-2)U(-2,\infty)$
(b) range $(-\infty,-3)$
(c) increasing $(-2,\infty)$
(d) decreasing $(-\infty,-2)$
Work Step by Step
To get the graph of $f(x)=\frac{-1}{(x+2)^2}-3$, shift $\frac{1}{x^2}$ to the left units, reflect across the x-axis, then shift down 3 units. See graph, we can identify the following:
(a) domain $(-\infty,-2)U(-2,\infty)$
(b) range $(-\infty,-3)$
(c) increasing $(-2,\infty)$
(d) decreasing $(-\infty,-2)$
