Finding the asymptotes

Question

Find the asymptotes for F(X) = ln(x²+3). I realise there is no vertical asymptote since X²= -3. I want to know if the horizontal asymptote exist

Answer 1

No, since $\lim_{x\to\pm\infty}F(x)=\infty$. Inded, if $M\in\Bbb R$ and $|x|>e^{M/2}$ then $F(x)=\ln(x^2+3)>\ln(x^2)>\ln e^M=M$.

Answer 2

You can easily draw a graph of this function by yourself or in any computer algebra system. It is clear that it has no asymptotes since logarithm isn't bounded and it increases infinitely.