**2019 SAJC P1 Q1**

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

(a)

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

[1]

(b)

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

[5]

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