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
Finding the asymptotes
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algebra-precalculus
graphing-functions
2 Answers
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No, since $\lim_{x\to\pm\infty}F(x)=\infty$. Inded, if $M\in\Bbb R$ and $|x|>e^{M/2}$ then $F(x)=\ln(x^2+3)>\ln(x^2)>\ln e^M=M$.
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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.
