enter the correct answer in the box. this graph represents a transformation of the parent cube root…

enter the correct answer in the box. this graph represents a transformation of the parent cube root function. replace the values of h and k to create the equation of the transformed function. $y = sqrt3{x - h}-k$

enter the correct answer in the box. this graph represents a transformation of the parent cube root function. replace the values of h and k to create the equation of the transformed function. $y = sqrt3{x - h}-k$

Answer

Explanation:

Step1: Identify the horizontal shift

The parent cube - root function (y = \sqrt[3]{x}) has its inflection - point at ((0,0)). The inflection - point of the given transformed function is at ((4, - 2)). The horizontal shift (h) of a function (y=\sqrt[3]{x - h}-k) is determined by the (x) - coordinate of the inflection - point. For a cube - root function, the form of horizontal shift is (x\to x - h). Since the inflection - point has moved 4 units to the right from (x = 0) to (x = 4), (h = 4).

Step2: Identify the vertical shift

The vertical shift (k) of the function (y=\sqrt[3]{x - h}-k) is determined by the (y) - coordinate of the inflection - point. The inflection - point has moved 2 units down from (y = 0) to (y=-2). In the equation (y=\sqrt[3]{x - h}-k), when (y=-2) at the inflection - point, and considering the general form of vertical shift, we have (-k=-2), so (k = 2).

Answer:

(y=\sqrt[3]{x - 4}-2)