Question

How do you find the domain and range of `sqrt(x-8)`?

Answer 1

Domain of `x` is `[8, infty)`
Range of `y` is `[0,infty)`

Explanation:

The square root is real only when the radicand is positive, or at least equal to zero. So the domain is going to be whenever

`x-8 >= 0`

`x >= 8`

Using interval notation, we say the domain of `x` is `[8, infty)`

The range is all the the `y` values that result from this domain. So the range starts at `x=8`

`y=sqrt(8-8)=sqrt(0)=0`

and goes up to infinity. Using interval notation the range of `y` is `[0,infty)`

You can also see this by inspection in the graph

graph{sqrt(x-8)[-1,17,-2,5]}