Final answer:
A rational function is a function that can be written in the form f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero.
Step-by-step explanation:
A rational function is a function that can be written in the form f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The numerator, P(x), and the denominator, Q(x), can both contain constants and variables. The graph of a rational function can have vertical asymptotes, horizontal asymptotes, holes, and x-intercepts.
For example, f(x) = (2x + 1)/(x - 3) is a rational function. The numerator, 2x + 1, is a polynomial of degree 1, and the denominator, x - 3, is a polynomial of degree 1. The graph of this rational function has a vertical asymptote at x = 3 and no horizontal asymptote.