The diagram below shows the graph of $y=\mathrm{f}\left( x \right)$. The graph has a minimum point

Question

The diagram below shows the graph of $y=\mathrm{f}\left( x \right)$. The graph has a minimum point at $\left( 1,3 \right)$ and intersects the axes at $x=-2$and $y=4$. The equations of the asymptotes are $y=2x$ and $x=-1$. On separate diagrams, sketch the graphs of $y=\mathrm{f}'\left( x \right)$,[2] $y=\frac{1}{\mathrm{f}(x)}$,[2]

Accepted Answer

(a)(i) Asymptotes $x=-1$ and $y=2$; intercept $(1,0)$. (ii) Asymptotes $x=-2$ and $y=0$; $y$-intercept $(0,1/4)$; maximum $(1,1/3)$; open point $(-1,0)$.

2013 TJC P1 Q7

2013 TJC P1 Q7

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