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

Jun 29, 2017

Domain of $x$ is $\left[8 , \infty\right)$
Range of $y$ is $\left[0 , \infty\right)$

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

$x - 8 \ge 0$

$x \ge 8$

Using interval notation, we say the domain of $x$ is $\left[8 , \infty\right)$

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 $\left[0 , \infty\right)$

You can also see this by inspection in the graph

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