## Exam Style Question## Worked solutions to typical exam type questions that you can reveal gradually |

Question id: 58. This question is similar to one that appeared in an IB Standard paper in 2014. The use of a calculator is allowed.

Let \(f(x)=\sin ( \frac {\pi}{4}x) + \cos ( \frac {\pi}{4}x) \), for \(-4\le x \le 4\)

(a) Sketch the graph of \(f\).

(b) Find the values of \(x\) where the function is decreasing.

(c) The function \(f\) can also be written in the form \(f(x)=a\sin ( \frac {\pi}{4}(x+c))\) where \(a\in \mathbf R\) and \(0 \le c \le 2\). Find the value of \(a\) and \(c\).

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