What is the range of x/√(x^2-x-2)?

Question

Find the range of x/√(x^2-x-2) without using calculator.

y = x/√(x^2-x-2)
y' = [x^2-x-2-x(2x-1)/2]/√(x^2-x-2)^3
= -(1/2)[x - 4]/√(x^2-x-2)^3
When x < -1, y'> 0, y is increasing.
When x > 4, y' < 0, y is decreasing.
When 2 < x < 4, y is increasing.

Answer 1

Vertical asymptotes at x=-1 and x = 2

Horizontal asymptote at y=-1 and y=+1
So range is (-infinity,-1) U (1, infinity)