The figure illustrates the graph of the function `y=f(x)` defined in [-3, 2].

Identify the correct statement(s)?

Options

A. Range of `y=f(-|x|)" is " [-2,2]`
B. Domain of `y=f(|x|)" is " [-2,2]`
C. Domain of `y=f|x|+1)" is " [-1, 1]`
D. Range of `y=f(|x|+1) " is " [-1,0]`

Answer

A, B, C, D

Explanation

(1) Graph of `y=f(-|x|)` is

` :. ` range is [-2, 2]
(2) Domain of `y= f(|x|)` is
`-3 le |x| le 2`
`implies -2 le x le 2`
(3) Domain of `y= f(|x|+1)` is
`-3 le |x|+1 le 2`
` implies -4 le |x| le 1`
`implies x in [-1,1]`
(4) Graph of `y=f(|x|+1)` is

` :. ` Range is [-1, 0]