The curve whose equation is \(y=3+\sqrt{1-4x}\) undergoes, in succession, the following transformations: A: Scaling by factor 2 parallel to the \(y\)-axis. B: Reflection in the \(y\)-axis. C: Translation of 6 units in the negative \(y\)-direction. Find the equation of the resulting curve.[3]
The diagram shows a sketch of the curve \(y=\mathrm{f}(x)\) with asymptotes \(x=2\) and \(y=3\). The curve has a maximum point \((-1.5,5)\), a minimum point \((-6,0)\) and passes through \((0,3)\) and \((1,0)\).
\(y=\mathrm{f}(|x|)\)[2]
\(y=\mathrm{f}'(x)\)[3]
On separate diagrams, sketch the following graphs indicating the coordinates of the points of intersection with the axes and the equations of the asymptotes, if any.
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Answer:Transformed equation \(y=2\sqrt{1+4x}\); sketches as shown