9709 - 8 marks | Maths4U

A reflected cosine over one cycle

8 written marks

Let \(f(x)=1-2\cos(3x)\), for \(\displaystyle 0\le x\le\frac{2\pi}{3}\).

State the amplitude, midline and least positive period of the unrestricted wave.

Sketch the graph on its stated domain. Label the endpoints, all extrema and both \(x\)-intercepts.

Solve \(f(x)=2\) on the same domain.

Complete-answer checking, worked solutions and indicative written criteria.