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

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Answer 1 · 2017-06-29T16:23:05

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

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]}