Vertical Translation of Function Graphs: f(x)+k Dynamic Demo

This example demonstrates the vertical translation transformation of function graphs. By using a slider to control parameter k, students can observe how the function f(x) moves upward or downward in real-time. The core mathematical concept is the translation rule: f(x)+k shifts the original graph vertically by |k| units—upward when k>0 and downward when k<0. Construction: Use Point command to create control points, Segment command for auxiliary lines, and slider object k to control the translation amount. Observe the relationship between original function f and translated images T1, T3, T4. Suitable for middle and high school mathematics teaching on function concepts, helping students understand translation rules for logarithmic, trigonometric, and other function types, also serving as an introduction to parameter transformations.