Final answer:
The function g(x) is a transformation of the cube root parent function. The options represent different transformations, including horizontal stretches, vertical translations, and vertical stretches or shrinks in the cube root function. In option B, g(x) = ∛(3x) + 3.
Step-by-step explanation:
The function g(x) mentioned in the question is a transformation of the cube root parent function, f(x) = ∛x. Comparing the options provided with the parent function, we can deduce the transformation applied to each option. For example, in option A, g(x) = ∛(3x), the cube root function is applied to the product of 3 and x, which suggests a horizontal stretch. However, this still follows the form of a cube root transformation.
In option B, g(x) = ∛(3x) + 3, in addition to the horizontal stretch, there is also a vertical translation. Options C and D introduce coefficients into the cube root, resulting in a vertical stretch in option C, g(x) = 3∛3x, and a vertical shrink in option D, g(x) = (1/3)∛3x. The act of cubing a number and considering fractional exponents links to the general understanding of exponential functions.