Problem

In the diagram, the graph with equation $y = f(x)$ is shown with solid lines and the graph with equation $y = g(x)$ is shown with broken lines.

(a) Describe fully a sequence of three transformations which transforms the graph of $y = f(x)$ to the graph of $y = g(x)$.

(b) Find an expression for $g(x)$ in the form $af(bx + c)$, where $a$, $b$ and $c$ are integers.