Questions relating to asymptotes

[MegaDeth]

Hello, I've just started learning about asymptotes in school. The questions I have are:

1. To find the vertical asymptote, why do you have to equal the denominator to 0? And then find x.
2. "" "" "" horizontal "" , why do you have to divide the numerator and denominator by x?

Thank you very much for your help, if anyone knows about a website or book that actually explains why you have to do certain things to achieve a result, I would be grateful for a recommendation.

 

[mathwonk]

well roughly speaking, vertial asymptotes occur when the graph goes up to infinity along a vertical line for form x=a. and in a rational function, that vertical line occurs at a root of the denominator.

horizontal asymptotes occur when the value of y has a finite limit as x--> infinity. as i recall that happens when the top and bottom of your fraction have the same degree. and the value of the limit of y equals the ratio of the leading coefficients of top and bottom.

to find that limit rigorously, one trick is to divide top and bottom by the lead power of x, and you see the limit occurring that way.