A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials such that q(x) ≠ 0. For example, f(x) = (x2 + x – 2) / (2x2 – 2x – 3) is a rational function and here, 2x2 – 2x – 3 ≠ 0.
We know that every constant is a polynomial and hence the numerators of a rational function can be constants also. For example, f(x) = 1/(3x+1) can be a rational function. But note that the denominators of rational functions cannot be constants. For example, f(x) = (2x + 3) / 4 is NOT a rational function, rather, it is a linear function.
