Answer
shift $\frac{1}{x^2}$ to the right 3 units, stretch vertically by a factor of 2, then reflect across the x-axis,
(a) domain $(-\infty,3)U(3,\infty)$
(b) range $(-\infty,0)$
(c) increasing $(3,\infty)$
(d) decreasing $(-\infty,3)$
Work Step by Step
To get the graph of $f(x)=\frac{-2}{(x-3)^2}$, shift $\frac{1}{x^2}$ to the right 3 units, stretch vertically by a factor of 2, then reflect across the x-axis. See graph, we can identify the following:
(a) domain $(-\infty,3)U(3,\infty)$
(b) range $(-\infty,0)$
(c) increasing $(3,\infty)$
(d) decreasing $(-\infty,3)$
