We know that for the parent function of a radical, #sqrt x#, the domain is #(0,oo)# since we can't put a negative number under the radical.

For this function, since we need a domain of #[3,oo)#, we can just put #x-3# under the radical. For any value smaller than three, we get a negative number under the radical.

Now the range: The range of the parent function is #(0,oo)# since we can't take a square root and end up with anything less than #0#. We need to reverse this so it's #(-oo,0]#. Reflect the function over the #y#-axis by putting a negative sign in front of the radical.

So we end up with #y=-sqrt(x-3)#

I hope that helps!