Compute Lipschitz constant of piecewise linear in $\Bbb R^d$.

Question

Suppose we define the piecewise linear functions in $[a, b]^d$ to be all functions that can be written in the form $f(x) = W_ix + b_i, $ if $ x\in A_i$ where $ \{A_i|i=1, ..., n\}$ is a finite partition of $[a, b]^d$, $W_i\in \mathbb{R}^d$ and $b_i\in \mathbb{R}^{d\times d}$. Are these functions Lipschitz functions? If yes, can we detect their constants? Thanks in regard.