Graphs of y=A sin[B(x-C)]+D: Transformations of Sine Functions

① This example dynamically illustrates the general sine function y=A sin[B(x-C)]+D, showing how parameters A, B, C, and D affect the graph's amplitude, period, phase shift, and vertical translation. ② Core mathematical concepts include trigonometric functions, horizontal and vertical translations, amplitude and period scaling, and reflection transformations of function graphs. ③ Construction details: The GeoGebra commands include LaTeX for formula text, with objects A, B, C, D as parameters, and multiple functions (f, g, h, h_1, i, j, k, l, m, n) along with text labels (text1, text2, text6) to display values. Sliders or input fields likely control the parameters, updating the graph in real time. ④ Suitable for high school trigonometry, pre-calculus, or function transformation lessons, ideal for classroom demonstrations or student-led exploration of how each parameter alters the sine curve.