# What is the domain and range of #y = sqrt(x-10) + 5#?

##### 1 Answer

Domain:

Range:

#### Explanation:

Let's start with the domain of the function.

The only restriction you have will depend on *real value* **only** if that number if **positive**, you need

which is equivalent to having

This means that any value of *smaller* than

As a result, the domain will be

The range of the function will depend on the *minimum value* of the square root. Since

For any

Therefore, the range of the function is

graph{sqrt(x-10) + 5 [-3.53, 24.95, -3.17, 11.07]}

**SIDE NOTE** *Move the focus of the graph 5 points up and 10 points to the right of the origin to see function.*