Putnam 1970 B5

Let $u_n$ denote the ramp function $$u_n (x) =\begin{cases} -n \; \text{for} \; x \leq -n, x \;\; \text{for} \; -n \leq x \leq n, n \; \text{for} \; n \leq x, \end{cases}$$ and let $f$ be a real function of a real variable. Show that $f$ is continuous if and only if $u_n \circ f$ is continuous for all $n.$