How to find the range of a function without a graph? Okay so I know how to find the domain of the function  $f(x) = \frac{3x^2}{x^2-1}$, which is $x\neq 1$ and $x\neq -1$, but I'm totally confused on how to find the range without using a graph.

Hint:
find for what values of $k$ the equation $k=\dfrac{3x^2}{x^2-1}$ has real solutions.
For $ x\ne \pm 1$ you have $ x^2= \dfrac{k}{k-3}$ so this fraction must be not negative: $\dfrac{k}{k-3}\ge 0$. The solution is the range.
