# How do you find the domain and range of  y= sqrt (x+4)/x?

Dec 24, 2016

Domain is any real value with $x \ge - 4 \mathmr{and} x \ne 0$
Range is any real value except $0$.

#### Explanation:

$y = \frac{\sqrt{x + 4}}{x}$. for finding domain under root should not be less than zero and denominator should not be zero.
Domain: $\left(x + 4\right) \ge 0 \mathmr{and} x \ge - 4 \mathmr{and} x \ne 0$

Domain (value of x) is any real value with $x \ge - 4 \mathmr{and} x \ne 0$
Range (value of y) is any real value except $0$. graph{(x+4)^0.5/x [-10, 10, -5, 5]}