# Find all asymptotes of a function: f(x)=log(x^2−4) Domain: xin(−infty,−2)cup(2,infty) Vertical asymptotes are x=−2 (left) and x=2(right): limx→ −2−log(x2−4)=−infty

Find all asymptotes of a function
Find all asymptotes of a function:
$f\left(x\right)=\mathrm{log}\left({x}^{2}-4\right)$
Domain: $x\in \left(-\mathrm{\infty },-2\right)\cup \left(2,\mathrm{\infty }\right)$
Vertical asymptotes are x=−2 (left) and x=2(right):

I calculate the limits in +/- infinity:

So I'm looking for the oblique asymptotes of a form y=Ax+B:

The same for $-\mathrm{\infty }$. How should I interpret this? There are no oblique asymptotes?
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umshikepl
Yes, there are no oblique asymptotes. In general there are when A and B are finite real numbers. In the particular case A=0 and B is a constant, then you find a horizontal asymptote.
The computations are correct.