Answer
Domain: $[6,\infty)$
Range: $[0,\infty)$
Work Step by Step
$h(x)=\sqrt{x-6}$
The expression under the square root must be greater than or equal to zero:
$x-6\geq0$
So the domain is $[6,\infty)$
The range of a square root function is $[0,\infty)$ (See graph)