Question

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

Answer 1

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

Explanation:

`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

Range: `(-oo, 0]`

Explanation:

`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]}