Course: Calculus I
Topic: Limits and Continuity
Subtopic: Continuity


Whether or not a function's graph has holes, jumps, or asymptotes is consequential to evaluating limits and performing other operations in calculus. These features of a graph are examples of discontinuities. The concept of continuous functions is the focus of this lesson. A function is continuous over its domain if and only if its graph can be drawn without removing your pencil from the paper.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: continuity, discontinuity, continuous at a point, continuous from the left/right, continuous on an interval, continuous everywhere, removable discontinuity, non-removable discontinuity, intermediate value theorem (IVT)

Text Notes

This a vital section full of important terminology and theorems. Study it thoroughly! To learn the theorems, it helps to physically write or type them in your own words.

Mini-Lectures and Examples

STUDY: Continuity

Supplementary Resources (optional)

Video: Continuity (including IVT), Selwyn Hollis's Video Calculus

Lesson: Continuous Functions, Dale Hoffman's Contemporary Calculus

Geogebra Exploration: Continuity at a Point, Mark Renault

rev. 2020-10-10