How do you find the asymptotes for f(x) = (x^2+4x-2)/(x^2-x-7)?
1 Answer
Jun 9, 2015
Explanation:
- Calculate Horizontal Asymptotes
lim_(x->+-oo)(f(x))=1
So we have a horizontal asymptote that isy=1 . - Calculate Vertical Asymptotes
x^2-x-7=0 ?
Delta_x=29
x_1= (-1+sqrt(29))/2 ; x_2= (-1-sqrt(29))/2
lim_(x->x_1)(f(x))=+oo
lim_(x->x_2)(f(x))=-oo
So we have two vertical asymptotes inx=x_1 and inx=x_2 - There aren't Oblique Asymptotes because there is a horizontal asymptote.
- For sure... Let's see the graph of
f(x)=(x^2-4x-2)/(x^2-x-7)
graph{(x^2-4x-2)/(x^2-x-7) [-10, 10, -5, 5]}