For this case we have the following function:
[tex]f (x) = - \sqrt {x + 3} -2[/tex]
By definition, the domain is given by all the values for which the function is defined.
The given function is no longer defined if the argument of the root is negative. So:
[tex]x + 3 \geq0\\x \geq-3[/tex]
Thus, the domain of the function is given by all the values of x greater than or equal to -3.
Domain: [-3, ∞)
Substituting the values of the domain, we find the range.
[tex]f (-3) = - \sqrt {-3 + 3} -2 = -2[/tex]
The function evaluated in ∞ gives -∞. So the range is given by:
(-∞, 2]
Answer:
Domain: [-3, ∞)
Range: (-∞, 2]
