The given options, g(x)= √x+2 (Option D) is the function that represents a transformation of the cube root parent function, although it's not an exact transformation of the cube root but rather a transformation of the square root function.
The cube root parent function f(x)=x^1/3 represents a function where the input value is raised to the power of 1/3. If you're looking for a transformation of this function, one common transformation involves adjusting the function by addition, subtraction, multiplication, or division to the original function.
Let's examine the provided options:
A. g(x)= √x represents a square root function, which is not a transformation of the cube root function.
B. g(x)= √x +2 is a square root function but adjusted by addition. It's not directly a transformation of the cube root function.
C. g(x)=2x represents a linear function (a straight line), which is not a transformation of the cube root function.
D. g(x)= √x+2 is a square root function adjusted by addition inside the square root. This is a transformation that shifts the original square root function horizontally by 2 units to the left.