<p>The diagram below shows the graph of $y=2\mathrm{f}\left( 3-x \right)$. The graph passes through the origin $O$, and two other points $A\left( -3,-\frac{9}{4} \right)$ and $\mathrm{B}\left( 3,0 \right)$. The equations of the vertical and horizontal asymptotes are $x=1$and $y=-2$respectively.</p>
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<ol class="abc-list"><li><div class="list-item-paragraph">State the range of values of $k$ such that equation $\mathrm{f}\left( 3-x \right)=k$ has exactly two negative roots.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">By stating a sequence of two transformations which transforms the graph of $y=2\mathrm{f}\left( 3-x \right)$ onto $y=\mathrm{f}\left( 3+x \right)$, find the coordinates of the minimum point on the graph of $y=\mathrm{f}\left( 3+x \right)$. Also, write down the equations of the vertical asymptote(s) and horizontal asymptote(s) of $y=\mathrm{f}\left( 3+x \right)$.<span class="inline-marks">[5]</span></div></li></ol>

The diagram below shows the graph of $y=2\mathrm{f}\left( 3-x \right)$. The graph passes through the origin $O$, and two other points $A\left( -3,-\frac{9}{4} \right)$ and $\mathrm{B}\left( 3,0 \right)$. The equations of the vertical and horizontal asymptotes are $x=1$and $y=-2$respectively.

State the range of values of $k$ such that equation $\mathrm{f}\left( 3-x \right)=k$ has exactly two negative roots.

By stating a sequence of two transformations which transforms the graph of $y=2\mathrm{f}\left( 3-x \right)$ onto $y=\mathrm{f}\left( 3+x \right)$, find the coordinates of the minimum point on the graph of $y=\mathrm{f}\left( 3+x \right)$. Also, write down the equations of the vertical asymptote(s) and horizontal asymptote(s) of $y=\mathrm{f}\left( 3+x \right)$.

2019 SAJC P1 Q1

2019 SAJC P1 Q1

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