Sketch the graph of \(f(x) = x + \frac{{8x}}{{{x^2} - 9}}\). Clearly mark the coordinates of the two maximum points and the two minimum points. Clearly mark and state the equations of the vertical asymptotes and the oblique asymptote.

     M1A1A1A1A1A1A1 

Note: Award A1 for both vertical asymptotes correct,

M1 for recognizing that there are two turning points near the origin,

A1 for both turning points near the origin correct, (only this A mark is dependent on the M mark)

A1 for the other pair of turning points correct,

A1 for correct positioning of the oblique asymptote,

A1 for correct equation of the oblique asymptote,

A1 for correct asymptotic behaviour in all sections.

[7 marks]

This question was generally well done, except for the behaviour near the origin. The questions alerted candidates to the existence of four turning points and an oblique asymptote, but not all reported back on this information.