N2009 P1 Q4

It is given that

\(f(x)=\begin{cases}7-x^2,&0<x\leq2,\\2x-1,&2<x\leq4,\end{cases}\)

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

1. Evaluate \(\mathrm{f}(27)+\mathrm{f}(45)\).[2]
2. Sketch the graph of \(y=\mathrm{f}(x)\) for \(-7\le x\le 10\).[3]
3. Find \(\int_{-4}^3 f(x)\,\mathrm dx\).[3]