Limits Continuity And Differentiability

Assertion (A) $f(x)=|x-a|+|x-b|$, is continuous on $\mathbf{R}$

Reason (R) $\frac{|x-\alpha|}{x-\alpha}$ is continuous at $x \in \mathbf{R}-\{\alpha\}$.

The correct option among the following is