Question

A function f(2)=√x is transformed into the function g (z) = 2√2-4+5. Name and explain in complete sentences the transformations that occurred to the parent cube root function.

Answer 1

The function g(z) appears to be derived from a cube root function through vertical stretching by a factor of 2, horizontal shifting to the right by 4 units, and vertical shifting up by 5 units, assuming the typo in the function g(z) is corrected.

Step-by-step explanation:

The student is asking about transformations of a function, specifically going from f(x) = √x to g(z) = 2√2 - 4 + 5. There seems to be a typo in the student's function g(z), so assuming a corrected version of the function as g(z) = 2√z - 4 + 5, the transformations are as follows:

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• Vertical Stretch: Multiplying by 2 stretches the graph vertically.
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• Horizontal shift: Subtracting 4 inside the radical shifts the graph to the right by 4 units.
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• Vertical shift: Adding 5 outside the radical shifts the graph upwards by 5 units.

Note that the parent function, the cube root function (often notated as f(x) = √x), has been modified through a series of transformations to create a new function g(z).