Extrapolation
Variable Fonts technology allows users to navigate between two or more specific styles (called masters or sources) with high precision and much smaller font file sizes than several static fonts.
When we navigate between masters—in the design space—we are looking at interpolations, and extrapolations go in the opposite directions.
For example, if we design a Regular and a Bold weight, a Medium can be interpolated between them. Using the same data, it could also be possible to extrapolate a Light weight, extending beyond the original scope of that weight axis.
It is not commonly used but some type design applications (or plug-ins) can generate previews of extrapolated instances.
GOING FURTHER
In a font editor software, extrapolation can be used to create new masters, helping extend the boundaries of the existing design space.
In a Variable Font, extrapolation can theoretically be used to preview areas of the design space (usually called corners) that haven't been defined by masters. Traditionally, you need at least 4 masters to define a design space of 2 axes. For example, a Regular and Bold on the weight axis, and a Condensed and Condensed Bold on the width axis. Mathematically, it should be possible to omit the Condensed Bold corner in the source, and still be able to generate a full functional VF out of the 3 other masters—Condensed Bold being extrapolated and not defined as a master. This makes it possible to manage complex design spaces while keeping the font file size reasonable.
Extrapolated results can be unreliable and visually disappointing, so they should be used with caution.
FONT ENGINEERING ADVICE
Functional Variable font extrapolations as described above were not really possible until the addition of the avar2 font table in 2024 in the OpenType Specifications. The table is still not widely supported yet and thus still at the experimental stage (as of the current version of Words of Type).