Graph-Sketching Strategy

Can you find out the following for this function

1. The Domain of f.
2. Whether f is even, odd or periodic (or none of these).
3. the x-intercepts and y-intercepts of f.
4. The intervals on which f is positive or negative.
5. The intervals on which f is increasing or decreasing, the nature of any stationary points, and the value of f at each of these points. 6. The asymptotic behaviour of f.

f(x) = x^2-4 / 1-x^2

Domain R - {-1, 1}

It's an even function.

y intercepts : x=0, y=-4

x intercepts : y=0, x=-2, 2

y' = (2x(1-x^2) + 2x(x^2-4)) / (1-x^2)
y' = 0
(2x(1-x^2) + 2x(x^2-4)) = 0
2x(1-x^2+x^2-4) = 0
2x(-3) = 0
x=0