Function Repository Resource:

IsContinuousFunction

Source Notebook

Determine whether a function is continuous

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["IsContinuousFunction"][expr,x,pt]

assesses whether expr is continuous, viewed as a real-valued function of x, at the point x=pt.

ResourceFunction["IsContinuousFunction"][expr,x]

assesses whether expr is continuous over the full set of real numbers.

ResourceFunction["IsContinuousFunction"][{expr,cond},x]

assesses whether expr is continuous, subject to condition cond.

Details and Options

A function

is continuous at a point c if

. The function f is continuous on

if it is continuous at every point

Examples

Basic Examples (2)

Test if a function is continuous over the Reals:

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Test if a function is continuous at a point:

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Scope (2)

One can explicitly specify a domain over which to test continuity:

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Omitting the condition on x produces a different result:

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Properties and Relations (1)

IsContinuousFunction uses the resource function FunctionDiscontinuities to determine the points of discontinuity of an expression:

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Publisher

Wolfram|Alpha Math Team

Version History

3.0.0 – 23 March 2023
2.0.0 – 23 July 2020
1.0.0 – 23 July 2020

Related Resources

Author Notes

To view underlying paclet code, evaluate the following: