Discuss the continuity of the function f(x) at x=0 were
$\displaystyle f(x) = \begin{cases} \frac{|x|}{x} & x \ne 0 \\ 1 & otherwise \end{cases}$
Since |x| = -x when x < 0 and x when x > 0 you should be able to see that f(x) = -1 when x < 0 and f(x) = 1 when x > 0. You should base your discussion on a simple sketch graph.