A counter shows the number n(x) = [x] + [-x] for a sensor reading x, where [t] is the greatest…

A counter shows the number $n(x) = [x] + [-x]$ for a sensor reading $x$, where $[t]$ is the greatest integer not above $t$. A technician watches the reading approach $3$ from below and from above. Find the limit of $n(x)$ as $x$ tends to $3$ from the left. Then find the limit as $x$ tends to $3$ from the right. Finally find the value of $n$ at exactly $x = 3$. Remember that $[-3.2] = -4$.