# What is the domain and range of #y = sqrt(x^2 + 2x + 3)#?

##### 1 Answer

Apr 25, 2016

With radical functions the argument under the root-sign and the outcome are always non-negative (in real numbers).

#### Explanation:

**Domain** :

The argument under the root sign must be non-negative:

We 'translate' by completing the square:

Which is always

So there are no restrictions to

**Range:**

Since the lowest value the argument can take is