Describing+asymptotic+behavior+in+terms+of+limits+involving+infinity

If x approaches a certain number as one goes to infinity and negative infinity, then there is a horizontal asymptote. If it only approaches infinty or negative infinity as it approaches positive/negative infinity, then there is no horizontal asymptote.

Ex: lim f(x)=7 x-->+/- infinity (There would be a horizontal asymptote at y=7)

There exists at horizontal asymptote at y=0 if the function given has some constant over x to a certain exponent.

Ex: lim 7/(x^3)= 0 or if the function was 6 - (function used before), then there would be an asymptote at 6 infinity