Rational functions are those of the form:
where p(x) and q(x) are polynomials. Their graphs often have vertical asymptotes where the denominator is zero. If the denominator is nowhere zero, there are no vertical asymptotes. Rational functions may also have horizontal asymptotes; these occur if f (x) approaches a finite number as x → ∞ or x → – ∞. The behavior of a function as x → ± ∞ is called its end behavior.