# What is the domain and range of the parent function f(x)=\sqrt{x} ?

The domain is D=[0,+\infty[ because $\setminus \sqrt{x}$ exists if and only if $x \setminus \ge q 0$.
The range is I=[0,+\infty[ too, because all real $y$ in [0,+\infty[ can be write $\setminus \sqrt{x}$ for an $x \setminus \in D$ (take $x = {y}^{2}$).
The domain $D$ is the projection of the curve on the x-axes.
The range $I$ is the projection of the curve on the y-axes.