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

Question

The diagram shows the graph of $y=\mathrm{f}\left( x \right)$. The curve passes through the origin, has a minimum point at $\left( -3,0 \right)$ and its equations of asymptotes are $x=-2$ and $y=2$. Sketch the following graphs on separate axes. $y=\frac{1}{\mathrm{f}\left( x \right)}$[3] $y=\mathrm{f}\left( -\left| x \right| \right)$[2] Describe a series of transformations that transforms the graph of ${{x}^{2}}+{{\left( y+1 \right)}^{2}}=1$ onto the graph of ${{\left( x-1 \right)}^{2}}+\frac{{{y}^{2}}}{9}=1$.[3]

Accepted Answer

(a)(i) Vertical asymptotes $x=-3$ and $x=0$, horizontal asymptote $y=\dfrac12$, hole at $(-2,0)$, no $x$-intercepts (a)(ii) Vertical asymptotes $x=\pm2$, horizontal asymptote $y=2$, minima $(-3,0)$ and $(3,0)$, also passing through $(0,0)$ (b) Translate $1$ unit in the positive $x$-direction, translate $1$ unit in the positive $y$-direction, then stretch by scale factor $3$ parallel to the $y$-axis

2019 RVHS Promo Q5

2019 RVHS Promo Q5

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