Continuity - AP® Maths Definition

What is continuity in AP® Calculus?

In the context of AP® Calculus, continuity refers to a fundamental property of a function that ensures it behaves in a predictable manner over its domain, without any breaks or jumps.

A function is said to be continuous at a point if three conditions are met:

• the function is defined at that point

• the limit of the function as it approaches the point from both sides exists

• and the limit equals the function's value at that point

A function is continuous on an interval if it is continuous at every point on that interval.

If a function is continuous at every point in its domain, then the function is simply said to be continuous.

Understanding continuity is crucial for analysing the behaviour of functions, particularly when dealing with derivatives and integrals, which require the function to be continuous over the intervals being considered.

Continuity study resources to ace your exams

Save My Exams has a great range of resources to help you explore the topic of continuity in more detail. Try this study guide on the topic, then have a go at some multiple choice and free response exam questions.

Explore our Calculus AB and Calculus BC study resources.