Find the range of the function f(x) = ((x^2 -4)(x-3))/(x^2-x-6).

Hello!
The range of a function is the set of its possible values.
The given expression for the function f is not so simple, let's try to simplify it. But first find the domain. There is a denominator, and it has not to be zero:
x^2 - x - 6 != 0, which gives x != -2 and x != 3 (easy to guess).
Therefore x^2 - x - 6 = (x+2)(x-3). The numerator has something in common:
(x^2-4)(x-3) = (x-2)(x+2)(x-3).
Thus the function becomes f(x) = ((x-2)(x+2)(x-3))/((x+2)(x-3)) = x-2, a simple expression. But remember that x != -2 and x != 3.
Now we can easily find the range. For x-2 when all x's are possible, it is the entire RR. Because x=-2 and x=3 are forbidden, the values y=-2-2=-4 and y=3-2=1 are impossible. So the range of f is RR\{-4,1}, which is
(-oo,-4) uu (-4,1) uu (1,+oo)
in interval notation.