Problem #558
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558
Functions f and g are such that
\(f(x) = 2 - 3 \sin 2x \quad \text{for} \; 0 \leq x \leq \pi,\)
\(g(x) = -2f(x) \quad \text{for} \; 0 \leq x \leq \pi.\)
(a) State the ranges of f and g.
The diagram below shows the graph of \(y = f(x)\).
(b) Sketch, on this diagram, the graph of \(y = g(x)\).
The function h is such that
\(h(x) = g(x + \pi) \quad \text{for} \; -\pi \leq x \leq 0.\)
(c) Describe fully a sequence of transformations that maps the curve \(y = f(x)\) on to \(y = h(x)\).
