Final answer:
The reciprocal parent function is f(x) = 1/x, which is option a) F(x) = 1/x from the given choices.
Step-by-step explanation:
The reciprocal parent function in mathematics is represented by f(x) = 1/x. This function is the one where the output value is the reciprocal of the input value. It is a function that has different characteristics compared to linear, quadratic, and other types of functions. For instance, in the given options, f(x) = |x| represents an absolute value function which is V-shaped and not a reciprocal function. f(y) = x^3 is a cubic function with an S-shaped curve. f(x) = -x is a linear function with a negative slope. Therefore, the correct choice that represents the reciprocal parent function is a) F(x) = 1/x.