Find Vertical Asymptote
Here is another review question placed on the board by my teacher.
Find the vertical asymptote(s) of the function
G(x) = (x^3 - 1)/(x - x^2)
He said the only vertical asymptote is x = 0.
However, I disagree.
I say that x = 1 is another asymptote.
HERE IS MY WORK:
I factored the denominator.
x - x^2 = x(1 - x).
I then set each factor to 0 and solve for x.
One factor is x = 0
I also set 1 - x = 0 and got x = 1 as another asymptote.
My teacher said that I am wrong but gave me credit for trying.
Who is right and why?
Your Teacher is Right, because, the curve has Vertical Asymptote x = 0. It also has one Linear Oblique Asymptote, y = - x - 1
So, Linear Oblique Asymptote,
The value x = 1 is excluded from the graph, because it will make function undefined.
See the attached graph. Green line x = 0 is vertical Asymptote VA(y-axis)
Green dotted line (y = -x-1) is Linear Oblique Asymptote (LOA).