The graph of \(y = f(x)\) is transformed to the graph of \(y = 3 - f(x)\).
Describe fully, in the correct order, the two transformations that have been combined.
Solution
The transformation from \(y = f(x)\) to \(y = 3 - f(x)\) involves two steps:
1. Reflection in the x-axis: This changes \(y = f(x)\) to \(y = -f(x)\).
2. Translation 3 units in the positive y-direction: This changes \(y = -f(x)\) to \(y = 3 - f(x)\).
Alternatively, the transformations can be performed in reverse order:
1. Translation 3 units in the negative y-direction: This changes \(y = f(x)\) to \(y = f(x) - 3\).
2. Reflection in the x-axis: This changes \(y = f(x) - 3\) to \(y = 3 - f(x)\).
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