Question

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

Answer 1

The domain is `D=[0,+\infty[` because `\sqrt{x}` exists if and only if `x\geq 0`.

The range is `I=[0,+\infty[` too, because all real `y` in `[0,+\infty[` can be write `\sqrt{x}` for an `x\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.

graph{x^0.5 [-1, 9, -0.913, 4.297]}