2021 ACJC Promo Q4

The diagram shows the curve \(y=\mathrm{f}\left( x \right)\). There are two vertical asymptotes with equations \(x=-2\) and \(x=2\) respectively. The curve crosses the \(x\)-axis at the point \(A\) and has a maximum turning point at \(B\) where it crosses the \(y\)-axis.

The curve also has a minimum turning point at \(C\). The coordinates of \(A\), \(B\) and \(C\) are \(\left( a,0 \right)\), \(\left( 0,-10 \right)\) and \(\left( p,q \right)\) respectively, where \(a\), \(p\) and \(q\) are constants

Sketch the following curves and state the equations of the asymptotes, the coordinates of the turning points and of points where the curve crosses the axes, if any. Leave your answers in terms of \(a\), \(p\) or \(q\) where necessary.

1. \(y=\frac{1}{\mathrm{f}\left( x \right)}\), and[3]
2. \(y=\mathrm{f}\left( 2-\left| x \right| \right)\). .[3]