The curve \(y=1-\mathrm{g}(x)\) has turning point \((a,b)\) and an asymptote \(x=c\), where \(a\), \(b\) and \(c\) are real constants. State the coordinates of the turning point and the equation of the asymptote of the curve \(y=\mathrm{g}(x)\).[2]
The diagram below shows the curve \(y=\mathrm{h}(x)\). The point \(A(-4,5)\) is a maximum point and the curve cuts the \(y\)-axis and \(x\)-axis at \(B(0,3)\) and \(C(2,0)\) respectively. It has asymptotes \(x=4\), \(y=0\) and \(y=3\).
On separate diagrams, sketch the graphs of
\(y=\mathrm{h}(|x|)\),[2]
\(y=\dfrac{1}{\mathrm{h}(x)}\).[3]
In each case, indicate clearly the equations of the asymptotes, and the coordinates of the axial intercepts and of the points corresponding to \(A\), \(B\) and \(C\), whenever possible.
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Answer:Turning point \((a,1-b)\), asymptote \(x=c\); transformed graphs as shown