For a rational function: $f(x) = \frac{numerator}{denominator}$

Provided that the numerator and denominator have no factors in common (if there are, we have "points of discontinuity" as discussed in the previous section), **vertical asymptotes** can be determined as follows:

$\bullet$equations of vertical asymptotes: x = zeros of the denominator

$i.e. f(x) = \frac{numerator}{x(x+5)(3x-7)}$; vertical asymptotes: $x = 0, x = -5, x = \frac{7}{5}$