What is the domain and range of # y = 2sqrt(x - 3) - 3#?

1 Answer
Jul 28, 2016

Domain is determined by a square root, which is defined only for non-negative real numbers.
Therefore, domain of this function is #x >= 3#.

Function #y=2sqrt(x-3)-3# is monotonically increasing with #x# increasing from #x=3# to #+oo#.
At #x=3# the function equals to #-3#. Then, as #x# increases, it increases to #+oo#.
Therefore, range of this function is #-3 <= y <+oo#.