Final answer:
The transformed cube root function with a new inflection point at (3,-2) is represented by the equation f(x) = ∛(x - 3) - 2.
Step-by-step explanation:
The question asks us to write an equation for a transformed cube root function with a new inflection point at (3,-2). To achieve this transformation, we can translate the parent function f(x) = ∛x horizontally and vertically. The horizontal translation shifts the graph to the right by adding (x - h), where h is the x-coordinate of the new inflection point, and the vertical translation moves the graph up or down by adding k to the function, where k is the y-coordinate.
The transformed cube root function would be of the form f(x) = ∛(x - h) + k. Substituting the given inflection point (3,-2) into the equation, we get:
f(x) = ∛(x - 3) - 2
This equation represents the new cube root function with the inflection point at (3,-2).