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

##### 1 Answer
Apr 15, 2015

The domain of the function is $\left(- \infty , 2\right) \cup \left(2 , + \infty\right)$.

We can simplify in this way:

$y = \frac{\left(x - 2\right) \left(x + 2\right)}{x - 2} = x + 2$.

Since the range of $y = x + 2$ is $\mathbb{R}$, seems that the range is $\mathbb{R}$, but we have that $x \ne 2$ so the range is $y \ne 4$, because the graph is a line without the point $P \left(2 , 4\right)$.

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