Continuity at a point

Continuity at a point in mathematics means that a function behaves predictably and smoothly at that specific point. To be continuous, three conditions must be met: the function must be defined at that point, the limit of the function must exist as it approaches that point, and the value of the function at that point must equal the limit. In simpler terms, there should be no jumps, breaks, or holes in the graph of the function at that location, allowing for a seamless transition as you move along the curve.