The **join** of two varieties $X,Y\subseteq \mathbb{P}^n$ is
$$ J(X,Y) = \overline{\bigcup_{\substack{x\in X,~y\in Y\\x\ne y}} \ell(x,y)}$$
where $\ell(x,y)$ denotes the projective line through $x$ and $y$. The join of $k$ varieties $X_1,\ldots,X_k\subseteq \mathbb{P}^n$ is defined to be the closure of the union of the corresponding, projective $(k-1)$-folds, or by induction
$$J(X_1,\ldots,X_k) := J(X_1,J(X_2,\ldots,X_k))$$

This definition is from Joseph Landsberg's book *Tensors: Geometry and Applications*, page 118. The graph of a regular function is a projective variety, so this should be defined.