Answer
Graph
Work Step by Step
$$\eqalign{
& y = 2 - \frac{3}{{{x^2}}} \cr
& {\text{Find the }}y{\text{ intercept, let }}x = 0 \cr
& y = 2 - \frac{3}{{{{\left( 0 \right)}^2}}} \cr
& {\text{No }}y{\text{ - intercept}}{\text{.}} \cr
& {\text{Find the }}x{\text{ intercept, let }}y = 0 \cr
& 0 = 2 - \frac{3}{{{x^2}}} \cr
& 2{x^2} = 3 \cr
& x = \pm \sqrt {\frac{3}{2}} \cr
& x{\text{ - intercepts }}\left( { \pm \sqrt {\frac{3}{2}} ,0} \right) \cr
& \cr
& *{\text{Find the extrema}} \cr
& {\text{Differentiate}} \cr
& y' = \frac{d}{{dx}}\left[ {2 - \frac{3}{{{x^2}}}} \right] \cr
& y' = - \left( { - 6{x^{ - 3}}} \right) \cr
& y' = \frac{6}{{{x^3}}} \cr
& {\text{Let }}y' = 0 \cr
& \frac{6}{{{x^3}}},{\text{ there are no values at which }}y' = 0. \cr
& {\text{No relative extrema}}{\text{.}} \cr
& \cr
& {\text{*Calculate the asymptotes}} \cr
& 2 - \frac{3}{{{x^2}}} \cr
& {x^2} = 0 \to x = 0 \cr
& {\text{Vertical asymptotes at }}x = 0 \cr
& \mathop {\lim }\limits_{x \to \infty } 2 - \frac{3}{{{x^2}}} = 2 \cr
& \mathop {\lim }\limits_{x \to - \infty } 2 - \frac{3}{{{x^2}}} = 2 \cr
& {\text{Horizontal asymptote }}y = 2 \cr
& \cr
& {\text{*Symmetry}} \cr
& f\left( { - x} \right) = 2 - \frac{3}{{{{\left( { - x} \right)}^2}}} \cr
& f\left( { - x} \right) = 2 - \frac{3}{{{x^2}}} \cr
& f\left( { - x} \right) = f\left( x \right) \cr
& f\left( { - x} \right) = f\left( x \right){\text{ The function is even}} \cr
& {\text{Symmetry about the }}y{\text{ - axis}} \cr
& \cr
& {\text{Graph}} \cr} $$
