This was brought up by another student in one of my pre-calculus classes.
The graph was a simple quadratic $x^2$. The teacher stated that the graph was decreasing from $(-\infty,0)$, and increasing from $(0, \infty)$.
Why would zero not be included? i.e: decr. $(-\infty,0]$ and incr. $[0, \infty)$
Generally the $0$ is not included because the function is not decreasing (or increasing) at $0$.
It would be accurate, however to say that $y=x^2$ is non-increasing on the interval $(-\infty,0]$.