The diagram above shows the graph of $y=\mathrm{f}\left( x \right)$. It has a maximum point at \(\

Question

The diagram above shows the graph of $y=\mathrm{f}\left( x \right)$. It has a maximum point at $\left( 4,a \right)$, where $a>0$, and meets the axes at $\left( 1,0 \right)$ and $\left( 0,0.5 \right)$. The curve has asymptotes with equations $y=0$ and $x=-1$. On separate diagrams, sketch the graphs of $y=\frac{1}{\mathrm{f}\left( x \right)}$;[3] $y=\mathrm{f}'\left( x \right)$,[3] stating the equation(s) of any asymptotes and where possible, the coordinates of any turning point(s) and axial intercept(s).

Accepted Answer

(a) Vertical asymptote $x=1$, removable hole at $(-1,0)$, $y$-intercept $(0,2)$, no $x$-intercept or horizontal asymptote, minimum $\left(4,\frac{1}{a}\right)$ (b) Vertical asymptote $x=-1$, horizontal asymptote $y=0$, $x$-intercepts $(1,0)$ and $(4,0)$, $y$-intercept $(0,\mathrm{f}'(0))$ with $\mathrm{f}'(0)4$

2021 ASRJC Promo Q5

2021 ASRJC Promo Q5

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