Function Transformation Visualizer interactive tool
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 can change the base function and enter values for a, h, and k to compare the original and transformed graphs. This makes translations, stretches, compressions, and reflections easier to inspect in algebra and precalculus practice.
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.
Graph shifts, stretches, and reflections
This function transformation visualizer compares a base function with g(x) = a·f(x − h) + k. Adjust the parameters to inspect horizontal and vertical shifts, stretches, compressions, and reflections.
Need the formula or convention behind this result? Read the calculator methods and assumptions.