Asymptote Calculator
Find vertical, horizontal, and oblique asymptotes of rational functions. Enter the numerator and denominator polynomials.
Published by:
isCalculator Editorial Team
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How to use this tool?
Quick Start Guide
- Enter numerator coefficients – comma-separated numbers (e.g.,
2,3,1for2x²+3x+1). - Enter denominator coefficients – same format (e.g.,
1,0,-4forx²-4). - Click "Calculate Asymptotes" – results appear instantly.
What You Get
- Vertical asymptotes – from denominator roots (real only).
- Horizontal/oblique asymptotes – based on degree comparison:
- Numerator degree < denominator:
y = 0 - Equal degrees:
y = leading coefficient ratio - Numerator degree = denominator + 1: oblique asymptote from polynomial division
- Higher numerator degree: no horizontal/oblique asymptote
- Numerator degree < denominator:
For degrees > 2, roots are found numerically (Newton method). Ensure denominator is not all zeros.
Previous Results
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Frequently Asked Questions
Asymptotes are lines that a curve approaches arbitrarily closely as it tends to infinity. They can be vertical, horizontal, or oblique.
Enter the coefficients of the polynomial in descending order of degree, separated by commas. For example, for 2x^2 + 3x + 1, enter '2,3,1'.
It handles degrees up to any size, but root finding for higher degrees uses a numerical method and may not find all roots. For degrees 2 and below, exact roots are found.
