Question

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

Answer 1

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`.