Sine curve with a vertical shift: constant, transformations, sketch, inequality and number of roots

The function \(\mathrm{f}\) is defined by \(\mathrm{f}(x)=q-2\sin3x\) for \(0\le x\le\pi\), where \(q\) is a constant.

1. The least value of \(\mathrm{f}(x)\) is \(-1\). Find \(q\) and write down the range of \(\mathrm{f}\).[2]
2. Describe fully a sequence of transformations that maps the graph of \(y=\sin x\) onto the graph of \(y=\mathrm{f}(x)\).[2]
3. On the grid below, sketch the graph of \(y=\mathrm{f}(x)\).[2]
4. Solve the inequality \(\mathrm{f}(x)<0\).[2]
5. Find the set of values of \(k\) for which the equation \(\mathrm{f}(x)=k\) has
   1. exactly one solution,
   2. exactly four solutions.[2]