Question

How do you find the range of `f(x)=(x^2-4)/(x-2)`?

Answer 1

The domain of the function is `(-oo,2)uu(2,+oo)`.

We can simplify in this way:

`y=((x-2)(x+2))/(x-2)=x+2`.

Since the range of `y=x+2` is `RR`, seems that the range is `RR`, but we have that `x!=2` so the range is `y!=4`, because the graph is a line without the point `P(2,4)`.

graph{(x^2-4)/(x-2) [-10, 10, -5, 5]}