Vertical Dilations of the Square Root Graph

This example demonstrates the vertical dilation of the square root function y = √x, allowing users to dynamically adjust a parameter a to see how the graph is stretched or compressed vertically. The core mathematical concept is vertical dilation of function graphs: multiplying the function by a positive coefficient a scales every y-coordinate by a factor of a while keeping x-coordinates unchanged. Construction highlights: using GeoGebra's function object f to define the base square root function, a slider or parameter a to control the dilation factor, and text objects text1 and text1_1 to display the current function expression or explanatory notes for interactive observation. Suitable for middle school mathematics lessons on function transformations and graph properties, as well as pre-calculus review, helping students intuitively grasp how parameter changes affect function graphs.