A curve $C$ has equation $y=\dfrac{2x^2}{2x-1}$. Find the set of values that $y$ can not

Question

A curve $C$ has equation $y=\dfrac{2x^2}{2x-1}$. Find the set of values that $y$ can not take.[3] A curve $D$ has equation $y=\dfrac{4x^2+1}{2x-1}$. Express $y=\dfrac{4x^2+1}{2x-1}$ in the form $y=ax+b+\dfrac{c}{2x-1}$, where $a$, $b$ and $c$ are constants. Hence write down the equations of the asymptotes of $D$.[3] Describe a sequence of two transformations that transforms the graph of $y=x+\dfrac{1}{2x-1}$ onto $D$.[2]

Accepted Answer

(a) $0 < y < 2$ (b)(i) $y=2x+1+\dfrac{2}{2x-1}$, so $a=2$, $b=1$, $c=2$; asymptotes $x=\dfrac{1}{2}$ and $y=2x+1$ (ii) A scaling parallel to the $y$-axis with scale factor $2$, followed by a translation of $1$ unit in the positive $y$-direction

N2026 P1 Q8

N2026 P1 Q8