Visualizing an Infinite Limit of a Function at a Point

This GeoGebra example demonstrates the phenomenon of an infinite (diverging) limit: as the input approaches a specific point, the function values grow without bound, producing a clear visual “blow-up” behavior. The key math concepts are limits (infinite limits) and the asymptotic nature of a function near a point, supported by coordinated geometric construction. In the construction, GeoGebra commands such as Point and Segment are used to place crucial reference points and draw auxiliary segments. Function-related objects (e.g., f and g) together with parameters (e.g., a, alpha) define the approach point and the viewing direction. Additional geometric entities (A, B, C, D, h, i, F, l, BigA, p, G) and an equation/expression object (e.g., eq1) are used to organize constraints and encode the functional relationship, so the graph near the target point clearly indicates divergence. Suitable for secondary school to early university students studying limits and function graphs, especially for classroom visualization and self-study.