Hi!

Here is the question:

Graph the following rational function about the asymptotes- (x-2)/(x

^{3}-x

^{2}-x+1)

So I factored the denominator using the factor theorem, and found that x=1 is a factor of the cubic function. I then used long division to end up with a quadratic- (x

^{2}-1) , then I factored this difference of squares to (x+1)(x-1)

From what I can tell from this information is that the denominator is equal to (x-1)

^{2}(x+1) , which tells me that there are vertical asymptotes at x= 1, -1

My only problem is that when I checked my answer with a graphing calculator, it shows an odd curve in-between these asymptotes with a vertex at x= -0.5

Can anyone offer help in terms of graphing this rational function? I don't know how to mathematically conclude that the vertex of the curve inbetween the asymptotes is indeed at x= -0.5