函數

用父函數變換、平移後的倒數函數家族，以及同一個指數變化工作台，把圖像位移、漸近線、定義域斷裂、增長與衰減、以及目標時間問題維持在同一條可視化支線上，之後再延伸到局部變化與累積變化。

This page stays deliberately compact, but it now points toward a fuller math slice. Graph Transformations keeps one parent curve, one transformed curve, and a small set of landmark points in view so horizontal and vertical shifts, vertical scale, and reflections can be read as actual motion on the graph before the symbols get abstract. Rational Functions / Asymptotes and Behavior then keeps one shifted reciprocal family bounded on the same graph so vertical and horizontal asymptotes, domain breaks, intercepts, and an optional removable hole stay honest. Exponential Change / Growth, Decay, and Logarithms keeps one start value, one rate, one target, and one logarithmic inverse question on the same bench so doubling, half-life, and target time do not drift into detached algebra.