What is the domain and range of # y = (-4) / ( sqrt (x +1))#?

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Answer 1 · 2018-06-19T15:59:26

The domain is #x in (-1, +oo)#.
The range is #y in (-oo,0^-)#

The function is

#y=-4/sqrt(x+1)#

What's under the square root sign is #>=0# and also, the denominator #!=0#

Therefore,

#x+1>0#

#=>#, #x > -1#

The domain is #x in (-1, +oo)#

When #x->-1^+#, #=>#, #y->-oo#

When #x->+oo#, #=>#, #y->0^-#

The range is #y in (-oo,0^-)#

graph{-4/sqrt(x+1) [-7.1, 28.93, -12.47, 5.55]}