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Transformations of functions

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Learn it For y = a·f(x − h) + k: a stretches vertically (and reflects if negative), h shifts right, k shifts up. A point (x, y) on y = f(x) moves to (x + h, a·y + k).

Example: (2, 5) is on y = f(x). Where is it on y = 3f(x − 1) − 4?

x: 2 + 1 = 3.
y: 3(5) − 4 = 11.
(3, 11).

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