A function is discontinuous at a point if there is a sudden jump, break, or hole at that point in its graph. The function does not have a well-defined limit or the value of the function does not match the limit at that point.
Limit: The value that a function approaches as its input approaches some value.
Continuity: A property of functions where they are continuous at every point in their domain.
Removable Discontinuity: $\lim_{{x \to c}} f(x)$ exists but is not equal to f(c), often indicating a hole in the graph.