Question

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

Answer 1

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`