Vertical Asymptotes

A vertical asymptote is a vertical line the graph runs along toward infinity, occurring at a denominator zero whose factor does not cancel.

For r(x) = (x² − 9)/(x² + 5x + 6), the factor x + 2 survives simplification: near −2 the outputs explode — r(−2.1) = 51, r(−1.9) = −49.