2025 MI PU1 Promo Q2

The diagram shows the graph of \( y=\mathrm{f}(x) \). The curve has one vertical asymptote at \( x=-2 \) and one horizontal asymptote at \( y=2 \). The graph passes through the points \( (-3,0) \), \( (0,3) \) and has one turning point at \( (3,1) \).

Sketch the graph of \( y=\frac{1}{\mathrm{f}(x)} \), labelling the equations of any asymptotes and coordinates of the axial intercepts and turning point where applicable.[4]