What the app does
A one-sided limit that runs to infinity marks a vertical asymptote. A finite limit at ±∞ marks a horizontal one. Otherwise the slope m = lim f(x)/x is computed, and if it is finite and non-zero, q = lim [f(x) − mx] completes an oblique asymptote y = mx + q.
Why it matters
Asymptotes are the skeleton to draw first: sketch them, and the curve has far fewer places left to go. The degrees of a rational function predict which kind to expect before any limit is taken, which is a useful check on the answer.
Read further
- Asymptote Wikipedia
- Asymptote Wolfram MathWorld
- Limits at infinity and asymptotes OpenStax Calculus