Transformations of Graphs - Composite Transformations

The graph of \(y = \mathrm{f}(x)\) is shown below.

Sketch each of the following functions on separate diagrams, labelling the corresponding points after the transformations.

1. \(y = \mathrm{f}(x) - 2\)
2. \(y = -\mathrm{f}(x + 2)\)
3. \(y = \mathrm{f}(x - 1) + 2\)
4. \(y = \mathrm{f}(-x) - 3\)
5. \(y = \mathrm{f}(2x)\)
6. \(y = |2\mathrm{f}(x)|\)