The curve $C$ has equation $y=\dfrac{-3x^2+14x-13}{x-3}$. It is given that $C$ has an asy

Question

The curve $C$ has equation $y=\dfrac{-3x^2+14x-13}{x-3}$. It is given that $C$ has an asymptote $y=ax+b$, where $a$ and $b$ are constants. Find the values of $a$ and $b$.[2] Sketch $C$, stating the equations of any asymptotes and the coordinates of any turning points and points where the curve crosses the axes.[3] Curve $C$ undergoes the following sequence of transformations: Step 1: Translation of $2$ units in the negative $x$-direction Step 2: Scaling parallel to the $y$-axis by scale factor $\dfrac12$. Step 3: Reflection in $y$-axis Find the equation of the resultant curve.[3]

Accepted Answer

(a) $a=-3,b=5$. (b) Asymptotes $x=3,y=-3x+5$; no turning points; intercepts $\left(0,\dfrac{13}3\right),(1.28,0),(3.39,0)$. (c) $y=\dfrac32x-\dfrac12-\dfrac1{x+1}$.

2026 CJC Promo Q7

2026 CJC Promo Q7

Solution:

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