9 The function f is defined by
$$f ( x ) = \frac { x ^ { 2 } + 4 x } { x ^ { 2 } + 9 }$$
- The graph of \(y = \mathrm { f } ( x )\) has an asymptote which is parallel to the \(x\)-axis. Find the equation of this asymptote.
- Explain why the graph of \(y = \mathrm { f } ( x )\) has no asymptotes parallel to the \(y\)-axis.
- Show that the equation \(\mathrm { f } ( x ) = k\) has two equal roots if \(9 k ^ { 2 } - 9 k - 4 = 0\).
- Hence find the coordinates of the two stationary points on the graph of \(y = \mathrm { f } ( x )\).
| Surname | Other Names |
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June 2005
Advanced Subsidiary Examination
MATHEMATICS
MFP1
Unit Further Pure 1
ASSESSMENT and
QUALIFICATIONS
ALLIANCE
Wednesday 22 June 2005 Afternoon Session
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