Problem

The diagram shows the graphs of $y=x^3$ and $y=f(x)$. The graph of $y=x^3$ is transformed to the graph of $y=f(x)$ by a sequence of transformations.

(a) Describe fully a suitable sequence of transformations. Make clear the order in which the transformations are applied.

(b) You are given that $f(x)=a(x+b)^3+c$.

State the values of the constants $a$, $b$ and $c$.