# What is the domain and range of y= (sqrt (x+4))/x?

Nov 3, 2015

$x \setminus \in \left[- 4 , 0\right) \cup \left(0 , \infty\right)$
$y \in \left(- \infty , \infty\right)$

#### Explanation:

$x$ cannot be less than -4 due to square root of a negative number.
$x$ cannot be zero due to division by zero.

When $- 4 \le x < 0$, $- \infty < \setminus y \le 0$.
When $0 < \setminus x < \setminus \infty$, $0 < \setminus y < \setminus \infty$.