# How do you find the domain and range of #f(x)=sqrt(x-4)#?

##### 1 Answer

Here's what I got.

#### Explanation:

You know that when working with *real numbers*, you can only take the square root of a **positive number**.

This implies that the **domain** of the function, which includes all the values that *defined*, will have to account for the fact that

#x - 4 >= 0#

This is equivalent to saying that

#x >= 4#

You can thus say that the domain of this function is **all real numbers** that satisfy the above condition. In interval notation, this will be

The **range** of the function tells you the values that the function can take for values that

In this case, if you take the square root of a positive number, you will end up with a **positive number**, so

#f(x) = sqrt(x - 4) >= 0 color(white)(.)(AA) x in [4, +oo)#

The minimum value that

#f(4) = sqrt(4 - 4) = sqrt(0) = 0#

For any other value of

graph{sqrt(x-4) [-10, 10, -5, 5]}