# Exam Style Question

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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.

### Circular functions

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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