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

Parker Bird 2022-07-20 Answered
How do you find the domain and range of $\sqrt{x-8}$?
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Killaninl2
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
$x-8\ge 0$
$x\ge 8$
Using interval notation, we say the domain of x is $\left[8,\mathrm{\infty }\right)$
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 $\left[0,\mathrm{\infty }\right)$
You can also see this by inspection in the graph
graph{$\sqrt{x-8}\left[-1,17,-2,5\right]$}