Final answer:
The equation of the rational (reciprocal) parent function is f(x) = 1/x, represented by the choice C) f(x) = 1/x. This function shows inverse variation and is characterized by two asymptotes, with its graph being fundamental to understanding direct and inverse relationships in mathematics.
Step-by-step explanation:
The equation of the rational (reciprocal) parent function is f(x) = 1/x. This function is not a polynomial, but rather a type of rational function, which is a ratio of two polynomials. The parent function for a rational function represents the simplest case, where the numerator is 1 and the denominator is x. Therefore, the correct answer is C) f(x) = 1/x.
Rational functions and their graphs are an important part of high school algebra and pre-calculus curricula. The graph of this function features two asymptotes: a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. As x approaches 0 from either direction, the value of f(x) becomes very large in magnitude and can be either positive or negative depending on the direction from which x approaches 0. The function is undefined at x = 0 because division by zero is undefined in mathematics.
Understanding the behavior of rational functions, including the parent function f(x) = 1/x, can be critical in solving various mathematical problems that involve direct and inverse variation, as well as in understanding the real-world phenomena they can model, such as rates and densities.