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

Answer 1

Kennedy Adams

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 [-5, 5, 10, 10]} [Ans]

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Answer 2

Eva Adamson

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) [-2.322, 0.757, 1.953, -4.207]}

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Answer 3

Julia Adams

The range of the function (f(x) = -\sqrt{x + 3}) is ((-∞, 0]).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.