Horizontal and Vertical Translations of Functions

①This example demonstrates how a function's graph shifts horizontally and vertically, allowing users to visually explore the effects of translation parameters. ②The core mathematical concept is function transformation: a horizontal shift by h units yields f(x-h), and a vertical shift by k units yields f(x)+k, linking algebraic expressions to geometric movement. ③Construction: based on the summary, objects f, h, g, k, p are used; f is the original function, h and k likely represent translation amounts, while g and p are the translated graphs, created via GeoGebra's algebraic input and dynamic graphics. ④Suitable for middle and high school mathematics, particularly in function graphing and transformation units, serving as an interactive demonstration for teachers or a self-exploration tool for students to understand translation rules.