Function Repository Resource:

FunctionSigns

Determine the intervals on which a function is positive, negative or zero

Contributed by: Wolfram|Alpha Math Team
 ResourceFunction["FunctionSigns"][expr, x] returns an association of the values of x for which expr is positive, negative or zero. ResourceFunction["FunctionSigns"][expr, x, prop] returns a property of expr related to regions where expr is positive, negative or zero. ResourceFunction["FunctionSigns"][expr, x, {prop1, prop2, …}] returns an Association of the properties propi related to regions where expr is positive, negative or zero. ResourceFunction["FunctionSigns"][expr, x, All] includes all available properties.

Details

Available properties are "Positive", "Negative", "Zeros", "Discontinuities", "Regions", "Plot", "NumberLine" and "SignChart"

Examples

Basic Examples (2)

Find the regions where x2-4 is positive, negative or zero:

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Get several representations of information about the sign of x2-4:

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Scope (4)

Get a plot of a function colored to correspond to the sign of the output of the function:

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Get a sign chart that shows the intervals on which a function is positive, negative or zero:

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Discontinuities are indicated on the sign chart with vertical dots:

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If there are infinitely many places where a function changes signs, the visual outputs of FunctionSigns display information for an interval surrounding x = 0:

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Properties and Relations (1)

The function SignChart is available as a stand-alone resource function:

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Publisher

Wolfram|Alpha Math Team

Version History

• 2.0.0 – 23 March 2023
• 1.0.0 – 14 October 2022

Author Notes

To view the full source code for FunctionSigns, evaluate the following: