### Basic Examples

Basic Examples

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Find the parity of a basic power function:

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1

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Test another power function:

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-1

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Show that a constant function has even parity:

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1

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Find the parity of a rational function:

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-1

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Find the parity of the absolute value function:

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1

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Find the parity of a trigonometric function:

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1

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Find the parity of a gaussian function:

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1

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Test a signed gaussian function:

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-1

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Find the parity of the hyperbolic tangent function:

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-1

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Find the parity of the error function:

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-1

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Find the parity of a Fresnel integral:

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-1

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Find the parity of a shifted Fresnel integral:

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Undefined

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### Scope

Scope

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For a function of multiple variables, parity is determined based on the behavior of the function under the transformation . Find the parity of a function of two variables:

{x,y,..}{-x,-y,..}

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-1

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Find the parity of a function of three variables:

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-1

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Wrapping in converts this to an even function:

z

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1

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Show that an implicitly-defined circle is even in both and :

x

y

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1

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### Properties and Relations

Properties and Relations

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FunctionParity returns for functions that are neither even nor odd:

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Undefined

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The constant function is both even and odd:

f(x)=0

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0

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