# Do constant functions have asymptotes?

As far as I have learned a function has a horizontal asymptote $y = k$ if and only if $$\lim_{x \to \infty} f(x) = k$$ or $$\lim_{x \to -\infty} f(x) = k$$

Now, for a constant function $$f(x) = c$$ we have $$\lim_{x \to \infty} f(x) = \lim_{x \to -\infty} f(x) = c$$

Does this mean that all constant functions have horizontal asymptotes, or is this definition not the one commonly used?

$$f(x)=c$$
At only a countably infinite amount of times as $x\to\pm\infty$. But for all intended purposes, I think stating a constant function is asymptotic to itself, or indeed, that any function is asymptotic to itself, is, though not very useful, acceptably correct by standard definitions.
• That's not true. We can say $\sqrt{x^2+1}$ is asymptotic to $|x|$ as $x\to\pm\infty$, for example. More over, the function does not have to be defined everywhere. $$\lim_{x\to\infty}\frac1{\sqrt x}=0$$ – Simply Beautiful Art Nov 12 '16 at 14:48