# What are the asymptote(s) and hole(s), if any, of # f(x) =(-2x^2-6x)/((x-3)(x+3)) #?

Asymptotes at

Which we can write as:

Which reduces to:

So here,

For the horizontal asymptote, there exists three rules:

A graph confirms this:

graph{(-2x^2-6x)/((x+3)(x-3)) [-12.29, 13.02, -7.44, 5.22]}

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The function f(x) = (-2x^2-6x)/((x-3)(x+3)) has two vertical asymptotes at x = -3 and x = 3. There is a hole at x = -3.

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