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Transformations of Graphs - Composite Transformations

Transformations of Graphs - Composite Transformations

The graph of \(y = f(x)\) is given below.

  1. Describe the transformations involved for \(y = f(x - 2) + 1\).
  2. Sketch on the same diagram, the graph of \(y = f(x - 2) + 1\).
Graph of y = f(x)
Graph of y = f(x)

Solution:

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Answer:(a) Translate 2 units right, then 1 unit up. (b) Same-axis sketch shown; \((u,v)\mapsto(u+2,v+1)\).

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