Continuity and Three Types of Discontinuities

This GeoGebra example examines continuity and models the three types of discontinuities: removable, jump, and infinite discontinuities. It visually demonstrates how a function behaves near a point where the limit may fail to exist or where the function value differs from the limit. Core mathematical concepts include limits, left-hand and right-hand limits, continuity at a point, function values, and classification of discontinuities. The construction uses GeoGebra commands Function and Point, along with objects g, i, B, f, h, E, j, D, F, C, b, G, H, J, I, to build graphs that highlight holes, jumps, and vertical asymptotes. It is suitable for high school pre-calculus and introductory university calculus courses, supporting classroom instruction and independent student exploration of continuity and discontinuity in function graphs.