Final answer:
The parent function is f(x) = sqrt(x), representing the basic square root function. The transformations include a horizontal compression by a factor of 3, a horizontal shift left by 3 units, and a vertical shift downward by 4 units.
Step-by-step explanation:
The question asks us to identify the parent function and transformations applied to the given function: y = sqrt((1/3)x + 3) - 4.
Parent Function
The parent function is f(x) = sqrt(x), which represents the basic form of the square root function without any transformations.
Transformations
The transformations applied to the parent function are as follows:
Horizontal compression by a factor of 3, which can be seen from the coefficient 1/3 inside the square root.
Horizontal translation to the left by 3 units, which is deduced from the positive addition of 3 inside the square root.
Vertical translation downward by 4 units, which is indicated by the subtraction of 4 at the end of the function.
This function exhibits multiple transformations indicating that there is a horizontal stretch or compression accompanied by translations both horizontally and vertically.