Evaluate numerically:

RealAbs remains unevaluated for imaginary numbers:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate efficiently at high precision:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix RealAbs function using MatrixFunction:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Values of RealAbs at particular points:

Value at zero:

Values at infinity:

Evaluate symbolically:

Find values of for which :

Substitute in the value of to create pairs:

Visualize the result:

Plot :

Plot RealAbs along with its first derivative:

Plot RealAbs in three dimensions:

RealAbs is defined only for real inputs:

The range of RealAbs is the non-negative reals:

RealAbs is an even function:

RealAbs is not an analytic function:

It has a singularity at the origin but no discontinuities:

RealAbs is neither nondecreasing nor nonincreasing:

RealAbs is not injective:

RealAbs is not surjective:

RealAbs is non-negative:

RealAbs is convex:

TraditionalForm formatting:

First derivative:

Obtain an equivalent expression using the definition of derivative:

The function Abs of complex variables is not differentiable:

Higher derivatives:

Compute the indefinite integral using Integrate:

Verify the antiderivative:

Definite integral:

More integrals: