I hereby define the term Exterpolation.
Exterpolation: The generalization of "interpolation" and "extrapolation". Exterpolation unifies both meanings - which share identical equations, but over different domains - to also share identical domains. For example, both linear interpolation and extrapolation can use the "lerp" algorithm, but when
From: wiki/Extrapolation#Linear
If the two data points nearest the point
$x_*$ to be extrapolated are$(x_{k-1},y_{k-1})$ and$(x_k, y_k)$ , linear extrapolation gives the function:
$y(x_*) = y_{k-1} + \frac{x_* - x_{k-1}}{x_{k}-x_{k-1}}(y_{k} - y_{k-1}).$ (which is identical to linear interpolation if
$x_{k-1} < x_* < x_k$ )