Spotting the existence of asymptotes using calculus?

Question

Are there any requirements that when they are fulfilled (as far as the derivatives of a function are concerned) then a function will always have an asymptote?(a straight line asymptote)(for example one could guess that such a requirement that would automatically mean that the function has an horizontal (for example) line asymptote would be that the derivative of the function as x approaches infinity approaches zero but that is not true as in the example of the function f(x)=lnx it proves that a function can have zero derivative as x approaches infinity while the function does not have horizontal asymptote) If in my question above there do exist such requirements how can they be proven?