# How do you find the domain of 1/(x+2)?

May 13, 2017

You look for the values of $x$ that are outside the domain.

#### Explanation:

If $x = - 2$ then $x + 2 = 0$ so the denominator of the fraction will become indefinite.
Other values of $x$ are acceptable, so:

Domain $x \ne - 2$
Or in 'the language':
${\lim}_{x \to - {2}^{-}} y = - \infty$ and ${\lim}_{x \to - {2}^{+}} y = + \infty$

graph{1/(x+2) [-10, 10, -5, 5]}
As for range : as $x$ gets larger, the function will approach to $0$.

${\lim}_{x \to - \infty} y = {\lim}_{x \to + \infty} y = 0$

So range: $y \ne 0$