Describe a sequence of transformations which transforms the graph of $y=\frac{1}{x}$ on the graph

Question

Describe a sequence of transformations which transforms the graph of $y=\frac{1}{x}$ on the graph of $y=\frac{2x-1}{1-x}$.[3] A curve $L$ undergoes the following transformations: $ \qquad A$: Translation of $-2$ units in the direction of the $x$-axis, $ \qquad B$: scaling parallel to the $y$-axis by a factor of $3$, $ \qquad C$: translation of $4$ units in the direction of the $y$-axis. The equation of the resulting curve is $9{{x}^{2}}-4{{y}^{2}}+8y-40=0$. Determine the equation of the curve $L$.[4]

Accepted Answer

(a) Reflect in the $y$-axis, translate $1$ unit in the positive $x$-direction, then translate $2$ units in the negative $y$-direction (b) $L:\dfrac{(x-2)^2}{4}-(y+1)^2=1$

2022 NYJC Promo Q3

2022 NYJC Promo Q3

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