is there a simple way of seeing the local behavior of rational functions other than just plotting numbers.
pic related is [math]\frac{3x-4}{x^3-16}[/math] it factors into [math]\frac{3x-4}{x(x-4)(x+4)}[/math]
i marked the vertical and horizontal asymptotes with dotted lines. is there a way i could just tell that [math]f(x)\rightarrow0^-,x\rightarrow-\infty,f(x)\rightarrow0^+,x\rightarrow\infty[/math] from the function without plotting anything?