# Asymptote Calculator

> Analyze rational functions to find vertical asymptotes, horizontal asymptotes, slant (oblique) asymptotes, and removable discontinuities (holes).

**URL:** https://www.calculatoranswers.com/asymptote-calculator
**Category:** Education

## Quick Answer

Find the vertical, horizontal, and oblique (slant) asymptotes of any rational function by analyzing the degrees and roots of the numerator and denominator.

## Definition

An asymptote calculator analyzes rational functions to identify the lines that the graph of the function approaches. It determines vertical asymptotes by finding real roots of the denominator where the numerator is non-zero, classifies common roots as holes (removable discontinuities), finds horizontal asymptotes by comparing numerator and denominator degrees, and determines oblique (slant) asymptotes via polynomial long division.

## How to Use

1. **Enter the function** — Input the rational function with a division slash separating the numerator and denominator (e.g., (3x^2 - 2x) / (x^2 - 1)).
2. **Analyze poles and degrees** — The calculator finds the roots of the denominator and compares polynomial degrees.
3. **Review asymptotes list** — Read the horizontal, vertical, and slant asymptotes equations, along with step-by-step explanations.

## Disclaimer

This calculator provides estimates for educational and planning purposes. Always consult a qualified professional for specific advice on financial, medical, legal, or other regulated decisions.

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