# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Compute the discontinuities of a function of a single variable

Contributed by:
Wolfram|Alpha Math Team

ResourceFunction["FunctionDiscontinuities"][ computes the values of | |

ResourceFunction["FunctionDiscontinuities"][{ computes the | |

ResourceFunction["FunctionDiscontinuities"][…, computes points of discontinuity along with related information about each. |

ResourceFunction["FunctionDiscontinuities"] has the attribute HoldFirst.

ResourceFunction["FunctionDiscontinuities"] takes the option "ExcludeRemovableSingularities", having default value False, that determines whether to exclude removable discontinuities from the result.

A function *f*(*x*) is said to have a removable discontinuity at a point *x*=*a* if the limit of *f*(*x*) as *x*→*a* exists and is independent of the direction in which the limit is taken, but has a value that is different from *f*(*a*) (which may or may not be defined).

Compute the points of discontinuity of a rational function:

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Repeat the calculation, classifying the points of discontinuity:

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Compute the points of discontinuity of a trigonometric function:

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Repeat the calculation, classifying the points of discontinuity:

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Compute the points of discontinuity of a smooth function:

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Compute and plot the points of discontinuity of a rational function:

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Compute and plot the points of discontinuity of a step function:

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Compute and plot the points of discontinuity of a step function:

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Choose whether to exclude removable singularities:

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FunctionDiscontinuities has the attribute HoldFirst, enabling calculations such as the following:

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Points where a function approaches ±∞ are considered to be points of discontinuity, even if they are technically outside the range of function definition:

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- Discontinuity Calculator–Wolfram|Alpha Calculators
- Solve Discontinuous Function Problems with Wolfram|Alpha–Wolfram|Alpha Blog
- Discontinuity–Wolfram MathWorld
- Jump Discontinuity–Wolfram MathWorld
- Removable Discontinuity–Wolfram MathWorld
- Calculus–Wolfram|Alpha Products

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