(i)     Sketch the graph of \(y = f(x)\), clearly indicating any asymptotes and axes intercepts.

(ii)     Write down the equations of any asymptotes and the coordinates of any axes intercepts.

Find the inverse function \({f^{ - 1}}\), stating its domain.

     A1A1A1

Note:     Award A1 for correct shape, A1 for \(x = 2\) clearly stated and A1 for \(y =  - 3\) clearly stated.

x intercept (2.33, 0) and y intercept (0, –3.5)     A1

Note:     Accept –3.5 and 2.33 (7/3) marked on the correct axes.

[4 marks]

\(x =  - 3 + \frac{1}{{y - 2}}\)     M1

Note:     Award M1 for interchanging x and y (can be done at a later stage).

\(x + 3 = \frac{1}{{y - 2}}\)

\(y - 2 = \frac{1}{{x + 3}}\)   M1

Note:     Award M1 for attempting to make y the subject.

\({f^{ - 1}}(x) = 2 + \frac{1}{{x + 3}}\left( { = \frac{{2x + 7}}{{x + 3}}} \right),{\text{ }}x \ne  - 3\)     A1A1

Note:     Award A1 only if \({f^{ - 1}}(x)\) is seen. Award A1 for the domain.

[4 marks]