Describe a sequence of transformations which would transform a curve \(y=\mathrm{f}\left( x \right)\

Question

Describe a sequence of transformations which would transform a curve $y=\mathrm{f}\left( x \right)$ onto the curve $y=\mathrm{f}\left( 1-2x \right)$.[3] Sketch the graph of $y=\left| 2-3{{\mathrm{e}}^{x}} \right|$, showing the relevant features.[2] Without the use of a calculator, hence find the exact range of values of $x$ that satisfy the inequality $\left| 2-3{{\mathrm{e}}^{x}} \right|>{{\mathrm{e}}^{2x}}$, for $x\ge 0$.[4]

Accepted Answer

(a) MA translation of $1$ unit in the negative direction of the $x$-axis, A scaling parallel to the $x$-axis by factor $\frac{1}{2}$, A reflection about the $y$-axis. OR A scaling parallel to the $x$-axis by factor $\frac{1}{2}$, A translation of $\frac{1}{2}$ units in the negative direction of the $x$-axis, A reflection about the $y$-axis. (b) $ 0 < x < ln 2 $

2021 TJC Promo Q1

2021 TJC Promo Q1

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