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

Therefore, domain of this function is $x \ge 3$.
Function $y = 2 \sqrt{x - 3} - 3$ is monotonically increasing with $x$ increasing from $x = 3$ to $+ \infty$.
At $x = 3$ the function equals to $- 3$. Then, as $x$ increases, it increases to $+ \infty$.
Therefore, range of this function is $- 3 \le y < + \infty$.