Answer
Graph
Work Step by Step
$$\eqalign{
& y = 2 - x - {x^3} \cr
& {\text{Find the }}y{\text{ intercept, let }}x = 0 \cr
& y = 2 - \left( 0 \right) - {\left( 0 \right)^3} \cr
& y = 2 \cr
& y{\text{ - intercept }}\left( {0,2} \right) \cr
& {\text{Find the }}x{\text{ intercept, let }}y = 0 \cr
& 0 = 2 - x - {x^3} \cr
& {\text{Solving by a calculator}} \cr
& x = 1 \cr
& x{\text{ - intercept }}\left( {1,0} \right) \cr
& \cr
& *{\text{Find the extrema}} \cr
& {\text{Differentiate}} \cr
& y' = \frac{d}{{dx}}\left[ {2 - x - {x^3}} \right] \cr
& y' = - 1 - 3{x^2} \cr
& {\text{Let }}y' = 0{\text{ to find critical points}} \cr
& - 1 - 3{x^2} = 0 \cr
& 3{x^2} + 1 = 0 \cr
& {\text{No real solutions, there are no extrema}}{\text{.}} \cr
& \cr
& *{\text{Find the second derivative}} \cr
& y'' = \frac{d}{{dx}}\left[ { - 1 - 3{x^2}} \right] \cr
& y'' = - 6x \cr
& {\text{Let }}y''\left( x \right) = 0 \cr
& - 6x = 0 \cr
& x = 0 \cr
& {\text{Inflection point }}\left( {0,f\left( 0 \right)} \right) \cr
& y = 2 - \left( 0 \right) - {\left( 0 \right)^3} = 2 \cr
& {\text{Inflection point}} \to \left( {0,2} \right) \cr
& \cr
& {\text{*Calculate the asymptotes}} \cr
& {\text{No vertical asymptotes, the denominator is 1}}{\text{.}} \cr
& \mathop {\lim }\limits_{x \to \infty } \left( {2 - x - {x^3}} \right) = - \infty \cr
& \mathop {\lim }\limits_{x \to - \infty } \left( {2 - x - {x^3}} \right) = + \infty \cr
& {\text{No horizontal asymptotes}} \cr
& \cr
& {\text{Graph}} \cr} $$
