Worked Example 4

It is given that

\[\mathrm{f}(x) = \left\{ \begin{array}{ll} 4-2x & \text{for}\hspace{0.5em} 0 < x \le 2 \\ -(x - 4)^2 + 4 & \text{for}\hspace{0.5em} 2 < x \le 4 \end{array} \right.\]

and \(\mathrm{f}(x) = \mathrm{f}(x + 4)\) for all real values of \(x\).

1. Evaluate \( \mathrm{f}(17) + \mathrm{f}(-8)\).
2. Sketch the graph of \(y = \mathrm{f}(x)\) for \(-10 \le x \le 7\).