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

1 Answer
vince
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]}

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