Finding x-int, vertical and horizontal asymptotes of a rational function...???

To find y-int plug a 0 into the rational function.


How to find x-int, vertical and horizontal asymptotes?


x-int: find roots of numerator. (huh? roots?)


Hor.asym.: find roots of denominator. (huh? roots?)


vert.asym.:


a) if n%26lt;m then the x-axis is HA


b) if n%26gt;m there is no HA


c) if n=m then y=an/bn is HA


n? m? y=an/bn?


PLEASE HELP!!!

Finding x-int, vertical and horizontal asymptotes of a rational function...???
Consider the equation y= a (x^n) / b (x^m) where n and m are the highest powers of the variable x found AFTER factoring and reducing the numerator and denominator to the products of the smallest polynomials posible. The situation may be that n or m may be zero, and that's OK.


The y intercept is found when x=0. The x intercept is found when the factors of the numerator are set = to zero; i.e. if y= x^2 + 3x + 2 = (x+2) (x+1), then x=-2 and x=-1 are conditions that yield y=0, and -2 and -1 are the roots of the numerator and are the y intercepts.


The vertical asymptotes are when Y becomes infinite, i.e the denominator becomes zero. Take each of the factors in the denominator, set them equal to zero, and solve for the corresponding values of x. For an equation y = 6 / (x-2) (x+3), set each denominator factor equal to zero, and the conditions are for two vertical asymptotes, one at x=2, and the other at x= -3.


For the horizontal asymptotes go back to , y= (a (x^n)) / (b (x^m)). If n%26gt;m there is no HA. If n%26lt;m, such as y= x / ((x^2)+1), the HA is the x axis. If n=m the HA is an/bn, or just a/b.


Try this. I hope I didn't make any typo mistakes