In this activity, students explore discontinuities on function graphs using the TI-84 Evo. Through guided examples and problems, students investigate vertical asymptotes, removable discontinuities (holes), jump discontinuities, and other essential discontinuities — described both graphically and using limit notation. The TI-84 Evo's POI and Asymptote detection trace features serve as hands-on tools to visualize and classify these breaks across a variety of function types.

This lesson connects informal graphical intuition to the formal limit-based definitions of continuity and discontinuity. Students analyze rational, piecewise, and trigonometric functions to identify and classify discontinuities, and determine parameter values that ensure continuity, building essential foundational skills for calculus.