How do i go about identifying all horizontal and vertical asymptotes for a given problem?

Lets say (6x^2)/(x^3+2x^2-5x) for example, with multiple powers. How do I identify all of the asmpytotes?

 

And I was also curious, does every undefined value of f(x) lead to a vertical asymptote? Can the graph of of a function cross the graph of its horizontal or vertical asymptotes, and how many horizontal asymptotes can a graph have?

I have a few questions I am not sure on how to solve for my Math 141 lab....

1)Let f(x)=ax^2+bx+c if x<=50
dx+8 if x>50.

Find Constants{a,b,c,d} such that f(x) is continuous.
f(x) is differentiable.
f(x) has a local extremum of 100 at x=40.


2) Find the equation of the tangent line to the curve y^3+yx^2-3y^2=0 at the point 3,0.

3)Let f(x) = x^3cos(pi*x) find f30(4);