# How do you find the domain and range of #y = -sqrt( x^2- 3x -10)#?

##### 1 Answer

Domain:

Range:

#### Explanation:

**Finding the domain**

To find the domain, we want to look at when the function is defined. We can see that the function will not be defined in terms of real numbers if the value inside the square root is negative, so let's look at that inequality:

We can factor the left hand side:

We need to determine the intervals where this could be negative. They will be where the factors equal

This means that our intervals will be

Let's start with

In

And lastly, in

This means that the only time the expression in the square root is negative is when

**Finding the Range**

A square root can never put out a negative value, and since we concluded that our bits under the square root are defined up to infinity, we can conclude that the values of the square root will range from

However, we have a minus sign in front of the square root, so the range will instead be