Calculus
posted by Sachenka on .
Let
f(x)=(4x^2 7x +2)/(x^2 16x +63)
Find the equations of the horizontal asymptotes and the vertical asymptotes of f(x). If there are no asymptotes of a given type, enter NONE. If there is more than one asymptote of a given type, give a comma separated list (i.e.: 1, 2,...).

To find the vertical asymptotes, factorize the denominator (if possible) and determine the zeroes of the denominator. Here we find two at x=7 and x=9:
f(x)=(4x^2 7x +2)/(x^2 16x +63)
=(4x^2 7x +2)/((x7)(x9))
To find horizontal asymptotes, find the limit of the function as x>∞ or x>∞.
Lim f(x) x>∞
=Lim (4x²7x+2)/(x²16x+63)
=LIm (4x²/x²)
=4
Here we found a horizontal aysmptote at y=4 
find the vertical asymptotes of the graph of the function
g(x) = (4+X)/(X^2 (9XX)