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

Apr 16, 2017

Domain: $x \ge 4$
Range: $y \ge 0$

#### Explanation:

Any number inside a square root has to be positive or $0$ or else, the answer will be a complex solution. With that being said, $x - 4$ has to be greater than or equal to $0$:

$x - 4 \ge 0$

Solve this equation to find the domain. Add $4$ to both sides:

$x \ge 4$

So our domain is that x has to be greater than or equal to $4$.

Since the square root can never yield a negative number, $y$ will always be positive or $0$. So the range of $y$ is that:

$y \ge 0$