The diagram below shows the graph of $y=\mathrm{f}\left( x \right)$. The curve passes through the

Question

The diagram below shows the graph of $y=\mathrm{f}\left( x \right)$. The curve passes through the points $\left( -2,0 \right)$, $\left( 0,\frac{6}{5} \right)$ and $\left( 4,0 \right)$, and has turning points at $\left( -1,2 \right)$, $\left( 1,0 \right)$ and $\left( 3,4 \right)$. Sketch the graph of $y=\mathrm{f}\left( 2x+3 \right)$, indicating clearly the axial intercepts, stationary points and asymptotes (if any).[3] Sketch the graph of $y=\frac{1}{\mathrm{f}\left( x \right)}$, indicating clearly the axial intercepts, stationary points and asymptotes (if any).[3] Describe the sequence of transformations that will transform the graph of $y={{x}^{3}}$ to the graph of $y=1-8{{x}^{3}}$.[3]

Accepted Answer

(a)(i) $x$-intercepts $\left(-\dfrac52,0\right)$, $(-1,0)$, and $\left(\dfrac12,0\right)$, stationary points $(-2,2)$, $(-1,0)$, and $(0,4)$, no asymptotes (a)(ii) Vertical asymptotes $x=-2$, $x=1$, and $x=4$, horizontal asymptote $y=0$, minima $\left(-1,\dfrac12\right)$ and $\left(3,\dfrac14\right)$, $y$-intercept $\left(0,\dfrac56\right)$, no $x$-intercepts (b) Reflect in the $x$-axis, stretch by scale factor $8$ parallel to the $y$-axis, then translate $1$ unit in the positive $y$-direction

2022 ASRJC Promo Q8

2022 ASRJC Promo Q8

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