The transformations $A$, $B$ and $C$ are given as follows: $A$: A reflection in the $x$-ax

Question

The transformations $A$, $B$ and $C$ are given as follows: $A$: A reflection in the $x$-axis. $B$: A translation of $1$ unit in the positive $y$-direction. $C$: A translation of $2$ units in the negative $x$-direction. A curve undergoes in succession, the transformations $A$, $B$ and $C$, and the equation of the resulting curve is $y=\frac{2x+1}{2x+2}$. Determine the equation of the curve before the transformations, expressing your answer as a single fraction.[3] The diagram shows the curve $y=\mathrm{f}\left( x \right)$. The lines $x=-2$, $x=2$ and $y=\frac{3}{2}x$ are asymptotes to the curve. The curve has turning points at $\left( -3,-5 \right)$ and $\left( 3,5 \right)$. It also has a stationary point of inflexion at the origin $O$. State the range of values of $x$ for which the graph is concave downwards.[1] Sketch the graph of $y=\frac{1}{\mathrm{f}\left( x \right)}$.[2] Sketch the graph of $y={{\mathrm{f}}'}\left( x \right)$.[3]

Accepted Answer

(a) $\mathrm g(x)=\frac1{2x-2}$. (b)(i) $x<-2$ or $0<x<2$.

2024 DHS Promo Q6

2024 DHS Promo Q6

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