3.106: Cubic graph and modulus equations

The diagram shows the graph of $y = f(x)$, where $f(x)$ is a cubic. Find the possible expressions for $f(x)$.

On the axes, sketch the graphs of $y = |2x + 1|$ and $y = 4|x - 1|$, stating the coordinates of the points where the graphs meet the coordinate axes.

Find the exact solutions of the equation $|2x + 1| = 4|x - 1|$.