A) The parent function is f(x) = √x
This is true.
The parent function is the blue one. If you calculate the √ of the points 2, 4, 6, 8 and 10 you will see that the line represent the images.
B) The range of both function is y ≥ 3
False. The range of the red function is y ≥ 3 but the range of the blue function is y ≥ 0.
Remember that the range is the set of images of the functin.
C) The transformation of the parent function is √x + 3
True. When you add a constant to the function the graph shifts up the same numbe of units as the constant value.
D) The domain of both functions is x ≥ 0
True. The set of x-values is the domain. Those are the values for which the function is defined.