Holes

When you have a rational function where factors of the numerator and denominator cancel out, you are given a hole. at the factor of x put into the new cancelled formula.

Example

$f(x)=\frac{(x-3)(x+4)}{(x-7)(x+4)}$ Hole at x = -4 $f(x)=\frac{x-3}{x-7}$ $f(-4)=\frac{-4-3}{-4-7}=\frac{7}{11}$ There is a hole at $\left(-4,\frac{7}{11}\right)$