---
title: "Rational Functions — AP Calculus Definition & Exam Guide"
description: "A rational function is a ratio of two polynomials. In AP Calc, they drive limit manipulation, continuity questions, and partial fraction integration."
canonical: "https://fiveable.me/ap-calc/key-terms/rational-functions"
type: "key-term"
subject: "AP Calculus AB/BC"
---

# Rational Functions — AP Calculus Definition & Exam Guide

## Definition

Rational functions are functions that can be expressed as a ratio (fraction) of two polynomials. They have both a numerator and denominator, where neither can be zero simultaneously.

## Related Study Guides

- [1.12 Confirming Continuity over an Interval](/ap-calc/unit-1/confirming-continuity-over-an-interval/study-guide/HVxTuBB73RiPPODABBib)
- [6.12 Integrating Using Linear Partial Fractions](/ap-calc/unit-6/using-linear-partial-fractions/study-guide/VNjHMatlmaZoFyt7yLPH)
- [Unit 1 Overview: Limits and Continuity](/ap-calc/unit-1/review/study-guide/Y3NmqZtnvfKAdL2lDnaI)
- [1.6 Determining Limits Using Algebraic Manipulation](/ap-calc/unit-1/determining-limits-using-algebraic-manipulation/study-guide/rf9HZ2V3D6dDLvWD595E)

## Review

### Related Terms

- Polynomial Functions: Polynomial functions consist only of terms with non-negative integer exponents. They do not have any fractional or negative exponents.
- [Asymptotes](/ap-calc/key-terms/asymptotes): Asymptotes are lines that serve as boundaries for rational functions. They indicate where the graph approaches but never touches or crosses.
- Vertical Asymptote: A vertical asymptote occurs when the denominator in a rational function becomes zero, causing an undefined value at that point.