What are the domain and range of #y= 1+sqrt(x+3)#?

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Answer 1 · 2018-01-13T03:36:11

Domain: #[-3, +oo)# Range:#[1,+oo)#

#y= 1+sqrt(x+3)#

#y# is defined where #x+3>=0 -> x>=-3#

Hence, the domain of #y# is #[-3,+oo)#

#y# has a minimum value of 1 where #x=-3#

#y# has no finite upper bound.

Hence, the range of #y# is #[1,+oo)#

We can deduce these results from the graph of #y# below.

graph{1+sqrt(x+3) [-10, 10, -5, 5]}