In this case, the highest power of x is to the third power. We can divide both the numerator and the denominator by that power. The limit is undefined. So there is no horizontal asymptote. We can take the limit as x approaches infinity for this one as well.
Lets take the limit as x approaches negative infinity.
It approaches 0 from below but it still approaches 0. We have confirmed the three cases. Now lets try evaluating other limits. Sometimes this is all you need to do. Sometimes it is not possible to just evaluate the function because the function is not defined for that value.