Evaluate numerically:

Evaluate to high precision:

For inputs between -1 and 1, the precision of the output tracks the precision of the input:

For inputs outside that range, the result is exact:

Evaluate efficiently at high precision:

UnitTriangle threads over lists:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix UnitTriangle function using MatrixFunction:

Compute average-case statistical intervals using Around:

Values of UnitTriangle at fixed points:

Value at zero:

Evaluate symbolically:

Find a value of x for which UnitTriangle[x]=0.4:

Plot the UnitTriangle function:

Visualize scaled UnitTriangle functions:

Visualize the composition of UnitTriangle with a periodic function:

Plot UnitTriangle in three dimensions:

Function domain of UnitTriangle:

It is restricted to real inputs:

Function range of UnitTriangle:

UnitTriangle is an even function:

The area of the UnitTriangle is 1:

UnitTriangle is not an analytic function:

It has singularities:

However, it is continuous everywhere:

Verify the claim at one of its singular points:

UnitTriangle is neither nondecreasing nor nonincreasing:

UnitTriangle is not injective:

UnitTriangle is not surjective:

UnitTriangle is non-negative:

UnitTriangle is neither convex nor concave:

TraditionalForm typesetting:

First derivative with respect to x:

Higher-order derivatives with respect to x:

First derivative with respect to z:

Series expansion at the origin:

Compute the indefinite integral using Integrate:

Verify the anti-derivative away from the singular points:

Definite integral:

FourierTransform of UnitTriangle is a squared Sinc function:

FourierSeries:

Find the LaplaceTransform of UnitTriangle:

The convolution of UnitTriangle with itself: