# What is the domain and range of #y = -sqrt(x ^2 - 3x - 10)#?

##### 1 Answer

Domain: the union of two intervals:

Range:

#### Explanation:

Domain is a set of argument values where the function is defined. In this case we deal with a square root as the only restrictive component of the function. So, the expression under the square root must be non-negative for the function to be defined.

Requirement:

Function

Therefore, the domain of the original function is the union of two intervals:

Inside each of these intervals the expression under a square root changes from

Hence, the range of this function is