Final answer:
The parent function of c(x) = 3√x is the cube root function, which is represented as f(x) = ∛x (option c). This is identified by the fact that c(x) is a variation of the cube root function, only multiplied by a constant.
Step-by-step explanation:
The parent function of c(x) = 3√x can be identified by looking at the fundamental function that has been modified to obtain c(x). The function f(x) = √x is the square root function, f(x) = x² is the quadratic function, f(x) = ∛x is the cube root function, and f(x) = x is the linear function.
Since c(x) involves the cube root of x multiplied by a constant, the parent function is the cube root function, which means the correct answer is (c) f(x) = ∛x. Understanding parent functions is essential when analyzing transformations in functions, such as stretching or compressing. This concept is key in algebra and precalculus courses and can help with solving various mathematical problems.