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

1 Answer
Jun 29, 2017

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]}