Answer
(a) See graph (red).
(b) domain $\{x|x\ne-3\}$, range $\{y|y\lt2\}$.
(c) vertical asymptote $x=-3$, horizontal asymptote $y=2$.
Work Step by Step
(a) To obtain the graph of $y=2-\frac{2}{x^2+6x+9}=2-\frac{2}{(x+3)^2}$ from $y=\frac{1}{x^2}$, shift the curve 3 unit(s) to the left, stretch vertically by a factor of 2, reflect across the x-axis, then shift 2 units up. See graph (red).
(b) We can find the domain $\{x|x\ne-3\}$, range $\{y|y\lt2\}$.
(c) We can identify the vertical asymptote $x=-3$, horizontal asymptote $y=2$.
