1. Let's clarify the problem: An open point on a graph means the point is not included in the function's domain or range at that coordinate. 2. For example, if a function has a hole at $x=a$, it means $f(a)$ is undefined or not part of the function. 3. The function might approach a value near $x=a$, but the point $(a, f(a))$ is not included. 4. This is often represented graphically by a circle that is not filled in at that point. 5. Mathematically, if $\lim_{x \to a} f(x) = L$ but $f(a)$ is undefined or different from $L$, then there is an open point at $x=a$. 6. Open points indicate discontinuities or removable discontinuities in the function. 7. Understanding open points helps in analyzing limits and continuity of functions.