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

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Answer 1 · 2018-06-28T14:42:13

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

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]}