# Consider y = f(x) = (x-2) / (x+2), does this formula define a function for -3<x< 3?

Mar 28, 2017

No, the rational expression is undefined when $x = - 2$

#### Explanation:

When $x = - 2$, the numerator of $f \left(x\right)$ is $\textcolor{b l u e}{- 2} - 2 = - 4$ while the denominator is $\textcolor{b l u e}{- 2} + 2 = 0$.

So the formula would say:

$f \left(- 2\right) = - \frac{4}{0}$

which is undefined, since division by zero is (almost) always undefined.