Asymptote calculator

Find all asymptotes of a function — vertical (where it blows up), horizontal (long-run behavior), and oblique (slant).

f(x) =

Types of asymptotes

Vertical: x = a where the denominator is zero and the function is undefined. The graph shoots to ±∞.

Horizontal: y = L where f(x) → L as x → ±∞. Compare degrees: if deg(num) < deg(den), HA is y = 0. If equal, HA is y = leading coefficients ratio.

Oblique (slant): When deg(num) = deg(den) + 1. Found by polynomial long division.

Examples

f(x) = 1/(x−2): VA at x = 2, HA at y = 0.

f(x) = (2x+1)/(x−3): VA at x = 3, HA at y = 2.

f(x) = (x²+1)/(x−1): VA at x = 1, oblique y = x + 1.

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