= Solution
The explicit <divided difference> formula makes $M_i(t)$ a finite linear combination of $(t_j-t)_+^{k-1}$. It is therefore polynomial of degree at most $k-1$ between knots and globally $C^{k-2}$. For $t<t_i$, the nodal data come from a polynomial of degree $k-1$, whose order-$k$ divided difference vanishes; for $t\geq t_{i+k}$ all truncated powers vanish. Thus
$$
\boxed{\operatorname{supp}M_i=[t_i,t_{i+k}]},
$$
and normalization does not change the degree, smoothness, knots, or support.
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