Function transformations
Analyze a function to identify all transformations: shifts, stretches, compressions, and reflections from the parent function.
f(x) =
Transformation rules
Given parent f(x), the transformed function a·f(b(x−h))+k has:
h: Horizontal shift (right if h > 0). k: Vertical shift (up if k > 0).
a: Vertical stretch (|a| > 1) or compression (|a| < 1). Reflection over x-axis if a < 0.
b: Horizontal compression (|b| > 1) or stretch (|b| < 1). Reflection over y-axis if b < 0.
Example
2(x−3)²+1: Parent x². Right 3, up 1, vertical stretch by 2.
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