3. Given $f(x)=x^{2}-2 x+3, g(x)=k x-1$, then “ $|k| \leqslant 2$ ” is the ( ) condition for “ $f(x) \geqslant g(x)$ to hold for all $x \in \mathbf{R}$ ”.
(A) Sufficient but not necessary
(B) Necessary but not sufficient
(C) Sufficient and necessary
(D) Neither sufficient nor necessary
3. A.

Given $f(x) \geqslant g(x)$ always holds
$\Rightarrow x^{2}-(2+k) x+4 \geqslant 0$ always holds
$\Rightarrow(2+k)^{2}-4 \times 4 \leqslant 0$
$\Rightarrow-6 \leqslant k \leqslant 2$.