Graphs and transformations: JPJC 2024 Promo Q8

The diagram below shows the graph of $y=f(x)$. The curve passes through the points $A(-a,0)$ and $B(0,-a)$ and has a minimum point at $C(2a,-2a)$, where $a>0$. The lines $x=-2a$ and $y=-a$ are asymptotes of the curve.

On separate diagrams, sketch the graphs of

1. $y=f(x-a)+a$, [3]

2. $y=\dfrac1{f(x)}$, [3]

indicating clearly in each case, where appropriate, the equations of any asymptote(s), axial intercepts and coordinates of the points corresponding to $A$, $B$ and $C$.

The curve whose equation is $y=\sin x$, undergoes in succession, the following transformations:
$A$: A translation by $\pi$ units in the negative $x$-direction.
$B$: A scaling parallel to the $x$-axis by a factor of $3$.
$C$: A translation by $2$ units in the positive $y$-direction.the equation of the resulting curve. [3]