Vertical Translation: Shifting Function Graphs Up and Down

① This example demonstrates the vertical translation of a function graph, showing how adding or subtracting a constant to the function expression shifts the entire curve upward or downward, with intersection points moving accordingly. ② Core mathematical concepts include function graph transformations, vertical shifts, intersection points between curves and lines, and the relationship between algebraic changes and geometric movement. ③ Construction highlights: using GeoGebra's Intersect command to compute intersection points A and B between the function f and auxiliary lines a or g, and displaying coordinates or shift values via text1; a slider or parameter controls the vertical shift amount, enabling dynamic observation of graph and point movement. ④ Suitable for middle and high school mathematics (grades 8–12) when teaching function transformations, as well as introductory calculus or precalculus courses, fostering visual understanding of how constants affect function graphs and supporting inquiry-based learning.