posted by Lynn on .
Identify all horizontal and vertical asymptotes of the graph of the function. f(x)=x^2/x^2-4
I know the vertical asymptotes are x=2 and x=-2, but how do I find the horizontal asymptotes?
Just consider what happens when x gets large. At x = 10^100, say, all but the highest powers of x get swamped, so f(x) just looks like
x^2/x^2 = 1
So, y=1 is the horizontal asymptote
Or, you can do a polynomial division, to see that
x^2/(x^2-4) = 1 + 4/(x^2-4)
as x gets huge, 4/(x^2-4) goes to zero, leaving f(x) = 1.