A curve \(C\) has equation \((y-a)^2=x+1\), where \(a\) is a positive constant and \(a>1\).
Sketch \(C\), giving the coordinates of the vertex and any points where \(C\) crosses the \(x\)- and \(y\)-axes.[2]
\(C\) is reflected about the \(x\)-axis, followed by a translation of \(a\) units in the positive direction of the \(y\)-axis. Find the equation of the transformed curve, showing each transformation clearly.[2]
The curve \(y=\mathrm{f}(x)\) has a maximum point at \((-6,5)\), and it cuts the axes at \((-1,0)\), \((-3,0)\) and \((0,2)\). The lines \(y=4\) and \(x=-2\) are the asymptotes.
\(y=\mathrm{f}(|x|)\)[1]
\(y=\dfrac{1}{\mathrm{f}(x)}\)[3]
On separate diagrams, sketch the following graphs, giving the equations of the asymptotes and the exact coordinates of the axial intercepts and turning points.
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Answer:Transformed curve \(y^2=x+1\); required transformed graphs as shown