I am preparing to study for my exam, and there is something I am not sure about when evaluating the limit x --> Infinity of 4/x^2 - x Intuitively the function seems to go to minus infinity, and I wonder if that is a sufficient answer or am I overlooking a rigorous method that should be applied here. It doesn't seem sufficient because I am looking for a horizontal asymptote and this answer doesn't guide me to a definitive point where one exists although it implies there would be one. Can someone give me a clue as to the method that would get me a clear answer. Also as this function goes to 0, 4/0 is not defined so that's all I need to establish, right? And this would imply a vertical asymptote is at x = 0 which in turn implies that the function approaches infinity from above and below?