Question

What is the domain and range of `y= abs(x) - x`?

Answer 1

The domain is `x in RR`. The range is `y in [0,+oo)`

Explanation:

The domain is `x in RR`

By definition

`|x|`, `=>`, `{(=x " when " x>0),(=-x " when " x<0):}`

Therefore,

`y=`, `{(y=x-x=0" when " x>0),(y=-x-x=-2x " when " x<0), (y=0 " when "x=0 ):}`

Therefore,

The range is `y in [0,+oo)`

graph{|x|-x [-11.29, 14.02, -2.84, 9.82]}