a) Please see the graph. b) Both graphs have the same asymptotes--vertical: $x=0$, horizontal: $y=0$ c) Range of $1/x$: $(-infinity, 0)$ and $(0, infinity)$. Range of $1/x^2$: $(0, infinity)$
Work Step by Step
a) Green line: $y=1/x$, orange line: $y=1/(x^2)$ b) $y=1/x$ is the same as $y=1/x + 0$. Likewise, $y=1/(x^2)$ is the same as $y=1/(x^2) + 0$. Since these equations are the same with $+0$, the horizontal asymptote is $y=0$.