9

The graph of $y = f(|x|)$ for $-6\le x\le 6$ is shown below.

(a) On the following axes, sketch the graph of $y = |f(|x|)|$ for $-6\le x\le 6$.

It is given that $f$ is an odd function.

(b) On the following axes, sketch the graph of $y = f(x)$ for $-6\le x\le 6$.

It is also given that $\displaystyle\int_{0}^{4} f(|x|)\,dx = 1.6$.

(c) Write down the value of

(i) $\displaystyle\int_{-4}^{0} f(x)\,dx$;
(ii) $\displaystyle\int_{-4}^{4}\bigl(f(|x|)+f(x)\bigr)\,dx$.