What is the domain and range of #y = |x| + 5#?

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Answer 1 · 2018-07-03T05:12:55

The domain is #x in RR#. The range is #y in [5, +oo)#

The function is

#y=|x|+5#

For the absolute value, #x# can take any value.

Therefore, the domain is #x in RR#

The minimum value of #y# is when #x=0#

#=>#, #y=5#

And due to the presence of the asolute value, #y# can take only positive values as

#|-x|=x#

Therefore, the range is #y in [5, +oo)#

graph{|x|+5 [-56.73, 60.37, -20.6, 37.95]}