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Function Composition Visualizer

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About This MicroSim

Watch values flow through two function "machines" in sequence. The inner function g is applied first, then its output becomes the input to the outer function f. Use the Swap button to see how f∘g differs from g∘f!

Lesson Plan

Learning Objective: Students will explain how composite functions work by tracing values through two functions in sequence.

Key Discovery: Order matters! f(g(x)) is usually NOT the same as g(f(x)).