2019 SAJC P1 Q1

The diagram below shows the graph of \(y=2\mathrm{f}\left( 3-x \right)\). The graph passes through the origin \(O\), and two other points \(A\left( -3,-\frac{9}{4} \right)\) and \(\mathrm{B}\left( 3,0 \right)\). The equations of the vertical and horizontal asymptotes are \(x=1\)and \(y=-2\)respectively.

1. State the range of values of \(k\) such that equation \(\mathrm{f}\left( 3-x \right)=k\) has exactly two negative roots.[1]
2. By stating a sequence of two transformations which transforms the graph of \(y=2\mathrm{f}\left( 3-x \right)\) onto \(y=\mathrm{f}\left( 3+x \right)\), find the coordinates of the minimum point on the graph of \(y=\mathrm{f}\left( 3+x \right)\). Also, write down the equations of the vertical asymptote(s) and horizontal asymptote(s) of \(y=\mathrm{f}\left( 3+x \right)\).[5]