The function f(x) = \fracP(x)Q(x) represents a rational function, where P(x) and Q(x) are both polynomial functions. The numerator P(x) determines the values of f(x) based on the input x , while the denominator Q(x) affects the function's behavior, especially where it may be undefined, such as when Q(x) = 0 . Rational functions can exhibit various characteristics, including asymptotes and intercepts. Vertical asymptotes occur at the values of x that make Q(x) = 0 , while horizontal asymptotes describe the behavior of f(x) as x approaches infinity. Understanding these properties is essential in analyzing the function's graph and behavior.