Describe fully a sequence of transformations which transforms the curve $y^2 = x$ onto the curve \

Question

Describe fully a sequence of transformations which transforms the curve $y^2 = x$ onto the curve $\frac{y^2}{4} = 1 - x$.[2] A curve has equation $y = \mathrm{f}(x)$, where $$\mathrm{f}(x) = \begin{cases} 2\sqrt{1 - x} & \mathrm{for}\ 0 \le x < 1, \ 0 & \mathrm{otherwise}. \end{cases}$$ Sketch the curve of $y = \mathrm{f}(x)$ for $-2 \le x \le 2$, stating the coordinates of the end points and the coordinates of any points where the curve crosses the axes.[3] Sketch the curve with equation $y = \left| \mathrm{f}(x) - 1 \right|$ for $-2 \le x \le 2$, stating the coordinates of the endpoints and the coordinates of any points where the curve crosses the axes.[3]

Accepted Answer

(a) Translate the curve by $-4$ units in the direction of $x$-axis Reflect the curve in the $y$-axis Scale the curve by factor $\frac{1}{4}$ parallel to the $x$-axis

2023 NYJC Promo Q4

2023 NYJC Promo Q4