4x^2/(x^2-4) need domain and range... Im confused with this one

Question

anonymous · Answer

I thought domain was (-INF,-2)U(-2,2)U(2,INF)
and range (-INF,INF)  but its not, why?

anonymous · Answer

it skips some stuff

anonymous · Answer

domain is easy to find, range is a bear

anonymous · Answer

set 
$$y=\frac{4x^2}{x^2-4}$$ and solve the equation for $x$
you need help doing that?

anonymous · Answer

another way would be to look at the graph
it has a horizontal asymptote at $y=4$ and vertical ones at $x=-2$ and $x=2$
in the interval $(-2,2)$ the curve goes from $-\infty$ up to $0$
then it skips up to the horizontal asymptote of $y=4$ so the range is actually 
$$(-\infty, 0]\cup (4,\infty)$$

anonymous · Answer

I missed the bracket on zero in my original attempt.....what about the crazy domain

anonymous · Answer

the range is correct

anonymous · Answer

your domain is correct

anonymous · Answer

the range is what i wrote, not $(-\infty, \infty)$