Question $1(9$ points$)$

$3$

Given the rational function $y=\frac{x^3+3x^2-1}{x^3},$ determine its critical points, points of inflection, asymptotes and intercepts, then use this information to sketch a graph of the function. You MUST use graph paper for potential full marks.

Note: $,\frac{dy}{dx}=\frac{3(1-x^2)}{x^4},\frac{d^{2}y}{d{x}^2}=\frac{6(x^2-2)}{x^5}$

$[9]$