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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Transforming Periodic Graphs

Move, stretch, squish, and flip graphs

Note: Problems 5.13–5.17 refer to the graph of periodic function f(x) below.

5.13    Graph f(x) – 1.

It is helpful to identify key points on a graph before you attempt to transform it. For example, (–6,–2), (–4,2), (–2,–2), (0,2), (2,–2), (4,2), and (6,–2) may be considered key points on the graph of f(x) because they are the points at which f(x) changes direction.

When you transform a graph, think about the way in which the transformation affects the individual points you’ve identified. For example, to graph f(x) – 1, you subtract 1 from each of the f(x), or y, coordinates ...

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