The graph of $y = f(x)$ is shown below. For each point $(a, b)$ that is on the graph of $y = f(x),$ the point $\left( 3a - 1, \frac{b}{2} \right)$ is plotted, forming the graph of another function $y = g(x).$ As an example, the point $(0,2)$ lies on the graph of $y = f(x),$ so the point $(3 \cdot 0 - 1, 2/2) = (-1,1)$ lies on the graph of $y = g(x).$

(a) Plot the graph of $y = g(x).$ Include the diagram as part of your solution.

(b) Express $g(x)$ in terms of $f(x).$

(c) Describe the transformations that can be applied to the graph of $y = f(x)$ to obtain the graph of $y = g(x).$ For example, one transformation could be to stretch the graph vertically by a factor of $4.$