From the question we are asked to determine if the relation represents y as a function of x. If it is a function, find the domain and range.
y = √-x - 4
To determine if its a function, it has passed the vertical line test, so yes its a function.
if a vertical line touches the graph at more than one point then it's a function.
Domain of √-x - 4:
√f(x) ----> f(x) ≥ 0
solve for -x ≥ 0: x ≤ 0
Domain: x ≤ 0
For the range of √-x - 4
recall the range of a radical function of the form:
c√(ax + b) + k is f(x) ≥ k
k = -4
f(x) ≥ -4
So, Domain {x ≤ 0}: Range: {y ≥ -4}
So, the correct option is the third option which is {x ≤ 0}: Range: {y ≥ -4}
Grpah: