Answer:
domain: [-3, ∞)
range: [0, ∞)
(second option listed)
Step-by-step explanation:
(note, domain is the maximum range of x-values, range is the maximum range of y-values)
we know that whatever is inside a square root cannot be negative, so (x + 3) must end up to be greater than or equal to 0
x + 3 ≥ 0
-3 -3
so, x ≥ -3
the lowest value of x (the domain) is theoretically -3 (which it includes), we write this as :
[-3, ∞)
[includes -3]
(cannot include infinity, but can go up to infinity)
note: g(x) is y
and we know that we cannot get a real-number square root of less than 0 (so y also must be greater than or equal to 0)
which we express as this:
[0, ∞)
[includes 0]
(cannot include infinity)
so, the
domain: [-3, ∞)
range: [0, ∞)
(second option listed)
hope this helps!!
