What is the range of the function #f(x) = -sqrt(x+3)#?

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Answer 1 · 2017-06-16T10:33:09

Range : # f(x) <=0#, in interval notation: #[0,-oo)#

#f(x)= -sqrt(x+3)# . Output of under root is #sqrt(x+3)>=0 :. f(x) <=0# .

Range : # f(x) <=0# In interval notation: #[0,-oo)#

graph{-(x+3)^0.5 [-10, 10, -5, 5]} [Ans]

Answer 2 · 2017-06-16T10:48:03

Range: #(-oo, 0]#

#f(x) =-sqrt(x+3)#

#f(x) in RR forall (x+3) >=0#

#:. f(x) in RR forall x>=-3#

#f(-3) = 0# [A]

As #x# increases beyond all bounds #f(x) -> -oo# [B]

Combining results [A] and [B] the range of #y# is: #(-oo, 0]#

The range of #y# maybe better understood from the graph of #y# below.

graph{-sqrt(x+3) [-4.207, 1.953, -2.322, 0.757]}