Mike explains the important characteristics found in rational functions. A rational function is defined as a fraction with a polynomial in the numerator and a polynomial in the denominator. X-Intercepts: Found at x-values that make unique factors in the numerator zero Vertical Asymptotes: Found at x-values that make unique factors in the denominator zero Holes: Found at x-values that make common factors in the numerator and denominator zero. The y-coordinate is found by substituting that x-value in to the other factors. Horizontal Asymptotes: Depends on the degree of the numerator compared with the degree of the denominator.