The graph of \(y = f(x){\text{ for }} - 2 \leqslant x \leqslant 8\) is shown.

On the set of axes provided, sketch the graph of \(y = \frac{1}{{f(x)}}\), clearly showing any asymptotes and indicating the coordinates of any local maxima or minima.

     A1A1A1A1A1

Notes: Award A1 for vertical asymptotes at x = −1, x = 2 and x = 5 .

A1 for \(x \to - 2,{\text{ }}\frac{1}{{f(x)}} \to {0^ + }\)

A1 for \(x \to 8,{\text{ }}\frac{1}{{f(x)}} \to - 1\)

A1 for local maximum at \(\left( {0, - \frac{1}{2}} \right)\) (branch containing local max. must be present)

A1 for local minimum at (3, 1) (branch containing local min. must be present)

In each branch, correct asymptotic behaviour must be displayed to obtain the A1.

Disregard any stated horizontal asymptotes such as y = 0 or y = −1 .

[5 marks]

A large number of candidates had difficulty graphing the reciprocal function. Most candidates were able to locate the vertical asymptotes but experienced difficulties graphing the four constituent branches. A common error was to specify incorrect coordinates of the local maximum i.e. (0,–1) or (0,–2) instead of \(\left( {0, - \frac{1}{2}} \right)\). A few candidates attempted to sketch the inverse while others had difficulty using the scaled grid.