Transformations of Graphs - Recovering Original Graphs from Transformations

Transformations of Graphs - Recovering Original Graphs from Transformations

A curve, \(y = \mathrm{f}(x)\) undergoes the transformations A, B and C in succession:

A: a translation of 4 units in the positive direction of the x-axis.

B: a scaling parallel to the x-axis by a factor \(\frac{1}{3}\).

C: a translation of 2 units in the negative direction of the y-axis.

The equation of the resulting curve is \(y = e^{9x - 12} + 3x - 6\).

Find the equation of the curve \(y = \mathrm{f}(x)\).

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Answer:\(\mathrm f(x)=e^{3x}+x\)

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