What are the domain and range of the function #f(x) = -sqrt(x+3)-2#?

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Answer 1 · 2018-06-28T14:57:28

The domain is #x in [-3, +oo)#.
The range is #y in (-oo, -2]#

Let #y=-sqrt(x+3)-2#

What's under the square root sign is #>=0#

Therefore,

#x+3>=0#

#=>#, #x>=-3#

The domain is #x in [-3, +oo)#

When,

#x=-3#, #=>#, #y=-0-2=-2#

And

#lim_(x->+oo)-sqrt(x+3)-2=-oo#

Therefore,

The range is #y in (-oo, -2]#

graph{-sqrt(x+3)-2 [-7.06, 21.42, -7.46, 6.78]}