# How do you find the domain and range for #y = -sqrt ( x + 3)#?

##### 1 Answer

May 7, 2018

The domain is

The range is

#### Explanation:

The domain is

In fact, an even root exists if and only if its content is non negative. So, we must impose

As for the range, we can observe a some easy things:

- A square root is always positive, when it exists
- A square root is zero only when its content is zero. In our case, this happens only when
#x = -3# - A square root grows infinitely as its content grows infinitely

So, we know that