Logic and Function Geometric Transformations

This example dynamically demonstrates the interaction between functions and geometric figures, revealing the intrinsic connection between functional properties and geometric transformations. It involves core mathematical concepts including logical judgment, function definition, geometric transformations (translation, rotation), ratio relationships, and trigonometric function applications. Construction highlights include using RandomPolynomial to generate random polynomials, Coefficients to obtain coefficients, IsInteger to judge integer properties, If to implement conditional logic, and Root to find roots, creating objects such as f (function), l1 (line segment), a (point), text1/2 (text), button1 (button), and points A/B. It is suitable for high school mathematics teaching, used for function image analysis, geometric transformation exploration, and logical thinking training.