9231 P13 - Nov 2011 - Q10 - 13 marks
6564
A curve \(C\) has equation
\(y=\frac{5\left(x^{2}-x-2\right)}{x^{2}+5 x+10} .\)
Find the coordinates of the points of intersection of \(C\) with the axes.
Show that, for all real values of \(x,-1 \leqslant y \leqslant 15\).
Sketch \(C\), stating the coordinates of any turning points and the equation of the horizontal asymptote.
[Question 11 is printed on the next page.]
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