How do you solve f(x)=(-3)/(x-2)^2?

Question

We are looking for the vertical and horizontal asymptotes. How would I solve it when the whole bottom half is squared?

I get that you set the denominator to 0 to find the vertical, but how do I do that here? Do I set two problems equal or do I do 'complete the square' or something else?

And I know that the equation is Anx^n/Bmx^m and that

n<m then y=0

n=m then a/b

but my teacher didn't tell us what to do if n>m

Thank you all so much for your help!

Answer 1

f(x) = -3 / (x - 2)²

Note that is x → ±∞, then (x - 2) → ∞, so that f(x) → 0.

So the horizontal asymptote is y=0.

Note that the denominator (x - 2)² is 0 at x = 2 and no other value. Also note the numerator is not 0.

Thus the only vertical asymptote is x = 2.