The domain of the function is:
x ≤ 5
The range is:
y ≤ -3
What is domain and range?
We want to find the domain and range of the function:
f(x) = -√(5 - x) - 3
The argument of a square root must be zero or larger, then the domain is defined by:
5 -x ≥ 0
5 ≥ x
For the range, when x = 5, we have the maximum of the function at:
f(x) = -√(5 - 5) - 3 = -3
And from there, as x decreases, the value of the function decreases, so the range is the set of all numbers equal to or smaller than -3
y ≤ 3