Set up a piecewise function with different pieces below and above zero:

Find the derivative of a piecewise function:

Use pw to enter  and and then TemplateBox[{ctrl, return}, Key1, BaseStyle -> {ExampleText, FontWeight -> Plain, FontFamily -> Source Sans Pro}] for each additional piecewise case:

Define a piecewise function:

Evaluate it at specific points:

Plot it:

Refine it under assumptions:

Automatic simplification of Piecewise functions:

Remove unreachable cases:

Remove False conditions:

Merge cases with the same values:

If values are not specified in a region, they are assumed to be zero:

This specifies that the default value should be 1:

Compute limits of piecewise functions:

Compute the limit in the direction of the positive imaginary axis:

Compute the series of a piecewise function:

Integrate a piecewise function:

Integration constants are chosen to make the result continuous:

Compute a definite integral of a piecewise function:

Laplace transform of a piecewise function:

Solve a piecewise differential equation:

Reduce a piecewise equation:

Integrating an implicitly piecewise integrand can give an explicit Piecewise result:

Symbolic minimization can give piecewise functions:

Compute the volume of an ellipsoid:

PiecewiseExpand converts nested piecewise functions into a single piecewise function:

Min , Max , UnitStep , and Clip are piecewise functions of real arguments:

Abs , Sign , and Arg are piecewise functions when their arguments are assumed to be real:

KroneckerDelta and DiscreteDelta are piecewise functions of complex arguments:

Boole is a piecewise function of a Boolean argument:

If , Which , and Switch can be interpreted as piecewise functions:

Convert Floor , Ceiling , Round , IntegerPart , and FractionalPart for finite ranges:

Convert Mod and Quotient when the number of cases is finite:

UnitBox and UnitTriangle are piecewise functions of real arguments:

Convert SquareWave , TriangleWave , and SawtoothWave for finite ranges:

BernsteinBasis and BSplineBasis are piecewise functions of real arguments:

Derivatives are computed piece-by-piece, unless the function is univariate in a real variable:

To specify that is real, use inequalities in the first condition:

This function is discontinuous at :