9709 - 8 marks | Maths4U

A tangent graph with a genuine break

8 written marks

Let \(\displaystyle g(x)=\tan(\frac x2-\frac\pi4)\) for \(0\le x\le2\pi\), excluding undefined inputs.

State the least positive period of the unrestricted function and find the zero and vertical asymptote in this interval.

Sketch the graph, labelling \((0,g(0))\), \((\pi,g(\pi))\), \((2\pi,g(2\pi))\), its zero and the asymptote.

Solve \(g(x)=-1\) on the stated domain.

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