Answer
shift $\frac{1}{x^2}$ to the right 4 units, reflect across the x-axis, then shift up 2 units,
(a) domain $(-\infty,4)U(4,\infty)$
(b) range $(-\infty,2)$
(c) increasing $(4,\infty)$
(d) decreasing $(-\infty,4)$
Work Step by Step
To get the graph of $f(x)=\frac{-1}{(x-4)^2}+2$, shift $\frac{1}{x^2}$ to the right 4 units, reflect across the x-axis, then shift up 2 units. See graph, we can identify the following:
(a) domain $(-\infty,4)U(4,\infty)$
(b) range $(-\infty,2)$
(c) increasing $(4,\infty)$
(d) decreasing $(-\infty,4)$
