The graph of \(y = f(x)\) is transformed to the graph of \(y = 2f(x - 1)\).
Describe fully the two single transformations which have been combined to give the resulting transformation.
Solution
The transformation from \(y = f(x)\) to \(y = 2f(x - 1)\) involves two steps:
1. Translation: The expression \(f(x - 1)\) indicates a translation of the graph by 1 unit in the positive x-direction.
2. Stretch: The factor of 2 in \(2f(x - 1)\) indicates a vertical stretch by a factor of 2.
Therefore, the graph is translated 1 unit to the right and then stretched vertically by a factor of 2.
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