Final answer:
The reciprocal parent function is represented by the equation F(x) = 1/x, which exhibits an inverse relationship between x and F(x), and is only defined for non-zero values of x.
Step-by-step explanation:
The term 'reciprocal' in mathematics refers to a number which, when multiplied by a given number, results in the product of 1. This concept is fundamental in understanding the relationship between multiplication and division. In the context of parent functions, the reciprocal parent function is best represented by the equation F(x) = 1/x. This is because the function represents the multiplicative inverse of x; for any non-zero value of x, its product with its reciprocal (1/x) is 1.
Considering the given options, the reciprocal parent function is A. F(x) = 1/x. This function is not defined at x=0 since division by zero is undefined in mathematics. The graph of this function has two asymptotes, the x-axis (y=0) and the y-axis (x=0), and it is present in both the second and fourth quadrants of the Cartesian plane, showing the inverse relationship between x and F(x).