---
title: "Continuous — AP Calculus Definition & Exam Guide"
description: "A function is continuous at a point when the limit exists and equals the function's value there. It's the hypothesis behind IVT, MVT, and differentiability on the AP exam."
canonical: "https://fiveable.me/ap-calc/key-terms/continuous"
type: "key-term"
subject: "AP Calculus AB/BC"
---

# Continuous — AP Calculus Definition & Exam Guide

## Definition

A function is continuous if there are no breaks, jumps, or holes in its graph. In other words, you can draw the graph of a continuous function without lifting your pencil.

## Related Study Guides

- [5.1 Using the Mean Value Theorem](/ap-calc/unit-5/using-mean-value-theorem/study-guide/79sP2PXcyvRvBsjb3HRq)
- [Unit 2 Overview: Differentiation](/ap-calc/unit-2/review/study-guide/HGq8OPntbFvqp1uRuEcj)

## Review

### Related Terms

- [Discontinuous](/ap-calc/key-terms/discontinuous): A function is discontinuous if it has breaks, jumps, or holes in its graph.
- [Limit](/ap-calc/key-terms/limit): The value that a function approaches as the input gets closer and closer to a certain point.
- [Intermediate Value Theorem](/ap-calc/key-terms/intermediate-value-theorem): If a continuous function takes on two different values at two points in an interval, then it must also take on every value between those two points within the interval.