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

1 Answer
Feb 13, 2015

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]}