How do you find the horizontal asymptote for #y = (x-4)^2/(x^2-4)#?

1 Answer
Feb 26, 2016

Answer:

Horizontal asymptote is #y=1#

Explanation:

#y=(x−4)^2/(x^2−4)# or #y=(x^2-8x+16)/(x^2−4)#

can also be simplified as #y=(x−4)^2/((x+2)(x-2))#

Hence vertical asymptote are #x=2# and #x=-2#

Fuether, as highest degree of numerator divided by highest degree of denominator is same, and ratio is given by

#x^2/x^2=1#

Horizontal asymptote is #y=1#