The graph with equation \(y = f(x)\) is transformed to the graph with equation \(y = g(x)\) by a stretch in the \(x\)-direction with factor 0.5, followed by a translation of \(\begin{pmatrix} 0 \\ 1 \end{pmatrix}\).

(a) The diagram below shows the graph of \(y = f(x)\). On the diagram sketch the graph of \(y = g(x)\).

(b) Find an expression for \(g(x)\) in terms of \(f(x)\).