The graph of $y=\mathrm{f}\left( 3-\frac{x}{2} \right)$ has $2$ stationary points at $\left( 8,-2 \r

Question

The graph of $y=\mathrm{f}\left( 3-\frac{x}{2} \right)$ has $2$ stationary points at $\left( 8,-2 \right)$ and $\left( 14,2 \right)$ and intersects the $x$-axis at $x=6$, $x=10$ and $x=18$ as shown in the diagram below. Sketch, on separate clearly labelled diagrams, the graphs of $y=\frac{1}{\mathrm{f}\left( 3-\frac{x}{2} \right)}$ $y=\mathrm{f}\left( x \right)$ Show clearly the asymptotes, stationary points and points of intersection with the axes in your diagrams.

Accepted Answer

(a) Sketch with asymptotes x=6, x=18, y=-1/4 (b) y=f(x) with asymptotes x=3, y=-4; key points (-6,0), (-4,2), (-2,0), (-1,-2), (0,0)

2009 AJC P1 Q11

2009 AJC P1 Q11

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