(3) Given $f(x)=x^{2}-2 x+3, g(x)=k x-1$, then “ $|k| \leqslant 2$ ” is “ $f(x) \geqslant g(x)$ holds for all $x \in \mathbf{R}$ ” ( ).
(A) A sufficient but not necessary condition
(B) A necessary but not sufficient condition
(C) A necessary and sufficient condition
(D) Neither a sufficient nor a necessary condition
(3) A Hint: $f(x) \geqslant g(x)$ always holds, i.e., $x^{2}-$ $(2+k) x+4 \geqslant 0$ always holds, thus we have $(2+k)^{2}-4 \times$ $4 \leqslant 0$, i.e., $-6 \leqslant k \leqslant 2$.