Answer
Graph
Work Step by Step
$$\eqalign{
& y = 3 + \frac{2}{x} \cr
& {\text{Find the }}y{\text{ intercept, let }}x = 0 \cr
& y = 3 + \frac{2}{0} \cr
& {\text{No }}y{\text{ - intercept}}{\text{.}} \cr
& {\text{Find the }}x{\text{ intercept, let }}y = 0 \cr
& 0 = 3 + \frac{2}{x} \to x = - \frac{2}{3} \cr
& x{\text{ - intercept }}\left( { - \frac{2}{3},0} \right) \cr
& \cr
& *{\text{Find the extrema}} \cr
& {\text{Differentiate}} \cr
& y' = \frac{d}{{dx}}\left[ {3 + \frac{2}{x}} \right] \cr
& y' = - \frac{2}{{{x^2}}} \cr
& {\text{Let }}y' = 0 \cr
& - \frac{2}{{{x^2}}} = 0,{\text{ there are no values at which }}y' = 0. \cr
& {\text{No relative extrema}}{\text{.}} \cr
& \cr
& {\text{*Calculate the asymptotes}} \cr
& 3 + \frac{2}{x} \cr
& x = 0 \to x = 0 \cr
& {\text{Vertical asymptote at }}x = 0 \cr
& \mathop {\lim }\limits_{x \to \infty } \left( {3 + \frac{2}{x}} \right) = 3 \cr
& \mathop {\lim }\limits_{x \to - \infty } \left( {3 + \frac{2}{x}} \right) = 3 \cr
& {\text{Horizontal asymptote }}y = 3 \cr
& \cr
& {\text{*Symmetry}} \cr
& f\left( { - x} \right) = 3 + \frac{2}{{\left( { - x} \right)}} \cr
& f\left( { - x} \right) = 3 - \frac{2}{x} \cr
& {\text{Neither odd nor even, so there is no symmetry}}{\text{.}} \cr
& \cr
& {\text{Graph}} \cr} $$
