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, C and D in succession:

A: Translation by 5 units in the positive x-direction.

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

C: Translation of 5 units in the negative y-direction.

D: Scaling by a scale factor of \(\frac{1}{3}\) parallel to the y-axis.

The equation of the resulting curve is

\(y = 3^{3x - 6} + \frac{1}{3}\cos(3x - 5) - \frac{5}{3}\).

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

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Answer:\(y=3^x+\cos x\)

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