How do these transformations change the graph of $f(x)$?

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The diagram shows the graph for \(y = f(x)\). The curve passes through the origin, and has a maximum point at \((1, 1)\). Sketch, on separate diagrams, the graphs of

1. \(y = f(x) + 2\),

2. \(y = f(x + 2)\),

3. \(y = f(2x)\),

giving the coordinates of the maximum point in each case.