Answer
$$\eqalign{
& {\text{Intercepts: none}} \cr
& {\text{Symmetry: }}x{\text{ - axis}} \cr
& {\text{There are no relative extrema}} \cr
& {\text{Vertical asymptote at }}x = 0 \cr
& {\text{Horizontal asymptote }}y = 0 \cr} $$
Work Step by Step
$$\eqalign{
& x{y^2} = 9 \cr
& {\text{Solve for }}{y^2} \cr
& {y^2} = \frac{9}{x} \cr
& {\text{The domain is }}x > 0,{\text{ because }}{y^2}{\text{ is always positive}}{\text{.}} \cr
& \cr
& {\text{Find the intercepts}} \cr
& *{\text{For }}y = 0 \cr
& {0^2} = \frac{9}{x},{\text{ Then there is no }}x{\text{ intercept}}{\text{.}} \cr
& *{\text{For }}x = 0 \cr
& {y^2} = \frac{9}{0},{\text{ Then there is no }}y{\text{ intercept}}{\text{.}} \cr
& {\text{Intercepts: none}} \cr
& \cr
& {\text{*Calculate the asymptotes}} \cr
& x{y^2} = 9 \cr
& {y^2} = \frac{9}{x} \cr
& {\text{Undefined at }}x = 0 \cr
& {\text{Vertical asymptote at }}x = 0 \cr
& {y^2} = \frac{9}{x} \to y = \pm \frac{3}{{\sqrt x }} \cr
& \pm \mathop {\lim }\limits_{x \to \infty } \frac{3}{{\sqrt x }} = 0 \cr
& {\text{Horizontal asymptote }}y = 0 \cr
& \cr
& *y = \frac{3}{{\sqrt x }} \to y' = - \frac{3}{{x\sqrt x }}, \cr
& y' = 0 \to {\text{ No solution.}} \cr
& {\text{There are no relative extrema}} \cr
& x{y^2} = 9 \Rightarrow {\text{ Symmetry: }}x{\text{ - axis}} \cr
& \cr
& {\text{Graph}} \cr} $$
