Question

The absolute value function, f(x) = –|x| – 3, is shown. What is the range of the function?

Answer 1

Range = [-3,-∞)

Explanation:

Let us see the parent function of

`f(x)=-\left | x \right |-3`

The parent function is

`f(x) =\left | x \right |`

`f(x)=-\left | x \right |-3`

is translated function. The parent function is reflected along x axis and then shifted down by three units.

please see the attached image.

The range of the parent function is All positive real numbers. Where as the range of translated function
`f(x)=-\left | x \right |-3` is negative real numbers , from -3 and onward

or

Range = [-3,-∞)