# What is the domain and range of #r(x)= -3sqrt(x-4) +3#?

##### 1 Answer

Aug 21, 2015

Domain:

Range:

#### Explanation:

Your function is defined for any value of **will not** make the expression under the square root **negative**.

In other words, you need to have

#x-4>=0 implies x>=4#

The domain of the function will thus be

The expression under the square root will have a *minimum value* at *maximum value* of the function

#r = -3 * sqrt(4-4) + 3#

#r = -3 * 0 + 3#

#r = 3#

For any value of

#r = underbrace(-3 * sqrt(x-4))_(color(blue)(<-3)) + 3 implies r < 3#

The range of the function will thus be

graph{-3 * sqrt(x-4) + 3 [-10, 10, -5, 5]}