Evaluate numerically:

Evaluate to high precision:

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

Evaluate efficiently at high precision:

Ramp threads over lists:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix Ramp function using MatrixFunction:

Values of Ramp at fixed points:

Value at zero:

Values at infinity:

Evaluate symbolically:

Find a value of x for which Ramp[x]1:

Plot the Ramp function:

Visualize shifted Ramp functions:

Visualize the composition of Ramp with a periodic function:

Plot Ramp in three dimensions:

Ramp is defined for all real numbers:

It is restricted to real inputs:

Function range of Ramp:

Ramp is equivalent to the average of a number with its RealAbs:

Ramp is not an analytic function:

It has singularities, but no discontinuities:

Ramp is nondecreasing:

Ramp is not injective:

Ramp is not surjective:

Ramp is non-negative:

Ramp is convex:

First derivative with respect to x:

Except for the singular point , this derivative is UnitStep:

Second derivative with respect to x:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integral:

FourierTransform of Ramp:

FourierSeries:

LaplaceTransform of Ramp:

The convolution of UnitStep with itself is equal to Ramp:

The convolution of Ramp and UnitStep gives a quadratic on the non-negative reals:

The convolution of Ramp with itself gives a cubic on the non-negative reals: