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**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

This definition requires three statements to hold true for * f(x)* to be continuous at

is defined, or**f(a)**is in the domain of**a****f(x)**- ,
must be defined on an open interval that contains**f(x)****a**:

Example 1: Discontinuous at a point

This function is discontinuous at * a = 3* since

Example 2: Discontinuous at the limit

This function is discontinuous at * a = 3* since

Example 3: Discontinuous at the function

This function has a discontinuity at * a = 3* since

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