Some of the content of this guide was modeled after a guide originally created by Openstax and has been adapted for the GPRC Learning Commons in October 2021. The graphs are generated using Desmos. This work is licensed under a Creative Commons BY 4.0 International License.
A function f(x) is continuous at a number a if
This definition requires three statements to hold true for f(x) to be continuous at a:
, f(x) must be defined on an open interval that contains a:
This function is discontinuous at a = 3 since f(3) is not defined.
This function is discontinuous at a = 3 since the limit of the function is undefined.
This function has a discontinuity at a = 3 since the limit of the function and the value of the function are not equal.
