Sketch the curve.

$y=x{e}^{-\frac{1}{x+1}}$

Only use technology if absolutely needed, and only then to approximate values. Do not use graphing technology.

Label the $y-$intercept, $x-$intercept$($s$)($if analytically possible$),$ all local extrema, and all inflection points on your final graph.

Use calculus to determine the behavior of the graph near any vertical asymptotes.

Use calculus to determine any horizontal or oblique asymptotes. If oblique asymptotes exist, prove that they are oblique asymptotes.

Be sure to graph any and all asymptotes.

Finally, credit is awarded for a clean, precise graph.