Function Transformation Visualizer interactive tool
Choose base function & transformation
Graph of f(x) and transformed g(x)
Base: Upward/downward opening parabola. The transformed function is g(x) = a·f(x − h) + k, where a = 1, h = 0, k = 0.
What Is Function Transformation Visualizer?
A function transformation visualizer shows how parameters in g(x) = a·f(x − h) + k change a base graph. By adjusting a, h, and k, you can see vertical stretches and compressions, horizontal and vertical shifts, and reflections.
Building Intuition for Transformations
Instead of memorizing rules in a table, students drag sliders and instantly see how the base function (like x² or |x|) moves or flips. This makes concepts like translating a parabola or reflecting an absolute value graph across the x‑axis far more intuitive, supporting algebra and precalculus coursework.
How To Use the Function Transformation Visualizer
- Choose a base function (linear, quadratic, or absolute value) from the dropdown.
- Enter values for a, h, and k to define the transformed function g(x) = a·f(x − h) + k.
- The visualizer will draw both the base function and the transformed function on the same axes.
- Observe how changing a stretches or flips the graph, while h and k shift it horizontally and vertically.
- Use the Example button to see a typical quadratic transformation, or Reset to return to the untransformed base graph.