Transform a supplied wave
7 written marks
On \([0,2\pi]\), the supplied graph \(y=f(x)=\sin x\) passes smoothly through \(\displaystyle (0, 0), (\frac{\pi }{2}, 1), (\pi , 0), (\frac{3\pi }{2}, - 1), (2\pi , 0)\), with no additional turning points. Its range is \([-1,1]\). Let \(g(x)=-3f(2x-\pi)+2\). All trigonometric features needed are given.
Part a · 2 marks
Give the coordinate mapping from \(f\) to \(g\).
Part b · 2 marks
Find the domain and range of \(g\).
Part c · 3 marks
Sketch \(g\), labelling the images of all five given points. Do not draw outside its domain.
Complete-answer checking, worked solutions and indicative written criteria.
Open the complete answer form