As x approaches 0 from negative side, f(x) approaches - infinity. As x approaches 0 from positive side, f(x) approaches positive infinity.
The slope of tangent of f(x) = f '(x) = 2 - 3/x²
Slope approaches minus infinity as x tends to zero. f(x) is discontinuous at x=0.
So the asymptote is x = 0 as the tangent at x=0 (slope is infinity) is perpendicular to x axis.
f ' (x) = Slope approaches 2, as x tends to infinity. So there is an asymptote with slope equal to 2 as x tends to infinity. we have to find its equation.
f(x) as x tends to infinity is : 2 x + 2 + 3/infinity or 2 x + 2
the second asymptote is y = 2x + 2