The curve $C$ has equation $y=\frac{{{x}^{2}}-5x+7}{4-2x}$. By expressing the equation of $C$ in the

Question

The curve $C$ has equation $y=\frac{{{x}^{2}}-5x+7}{4-2x}$. By expressing the equation of $C$ in the form $y=A\left[ \left( 3-x \right)+\frac{1}{\left( 3-x \right)+B} \right]$, where $A$ and $B$ are constants to be found, find a sequence of transformations which transforms the graph of $C$ on to the graph of $y=x+\frac{1}{x-1}$. [4] The diagram below the graph of $y=\mathrm{f}\left( x \right)$ with an asymptote $x=0.5$. The curve passes through the origin $O$ and has only one stationary point at $\left( 1,2 \right)$. Sketch the graph of $\frac{1}{\mathrm{f}\left( x \right)}$, showing clearly the equations of any asymptotes and the coordinates of any turning points and $x$- intercepts. [3]

Accepted Answer

(a) $A=\dfrac12$, $B=-1$; reflect in the $y$-axis, translate $3$ units right, then scale parallel to the $y$-axis by $2$ (b) Asymptotes $x=0$, $y=0$, turning point $(1,\dfrac12)$, removable hole $(0.5,0)$, no $x$-intercepts

2020 ASRJC P1 Q4

2020 ASRJC P1 Q4

Video Solution:

Solution:

Solution locked