Function Transformation Visualizer

See how the constants in g(x) = a·f(b(x − h)) + k stretch, flip, and slide a parent function. Drag the sliders — the graph and equation update live.

— — parent f(x) —— transformed g(x)

Parent
f(x) = x²

Transformed

Parent f(x):

vertical stretch a 1

horizontal stretch b 1

horizontal shift h 0

vertical shift k 0

Try: set a = −1 to flip over the x-axis, then slide h right and watch the graph translate by exactly h (not −h) — that sign reversal inside f(x − h) is the classic trap.