詳解：\(f(x) = \left| x \right|\) 可以分段定義如下

\(f(x) = \left\{ {\begin{array}{*{20}{c}}{ - x,x < 0}\\{x,x \ge 0}\end{array}} \right.\)

(1) 左極限 \(\lim\limits_{x \to {0^ - }} \left| x \right| = 0\)，右極限 \(\lim\limits_{x \to 0 + } \left| x \right| = 0\)，左極限與右極限相等，故 \(f(x) = \left| x \right|\) 是連續函數

(2)其圖形如下

故選(A)