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

Question

A curve, $y=\mathrm{f}(x)$ undergoes the transformations $A$, $B$, $C$ and $D$ in succession: Translation by $4$ units in the negative $x$ direction. Scaling by a scale factor of $2$ parallel to the $x$-axis. Reflection about the $y$-axis. A translation of $1$ unit in the positive direction of the $y$-axis. The equation of the resulting curve is $y=10-x+e^{\frac{x}{2}-4}$. Find the equation of the curve $y=\mathrm{f}(x)$.

Accepted Answer

$\mathrm f(x)=2x+1+e^{-x}$

Transformations of Graphs - Recovering Original Graphs from Transformations

Transformations of Graphs - Recovering Original Graphs from Transformations

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