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 $(3a- 7, -b + 3)$ is plotted, forming the graph of another function $y = g(x).$ As an example, the point $(-2,7)$ lies on the graph of $y = f(x),$ so the point $(2,22)$ lies on the graph of $y = g(x).$

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

(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 $4.$

tomtom Nov 26, 2023