2026 ASRJC P1 Q1

A graph with equation \(y=\mathrm{f}(x)\) undergoes, in succession, the following transformations:

1. A translation of 3 units in the negative \(y\)-direction;
2. A translation of 1 unit in the negative \(x\)-direction;
3. A scale parallel to the \(x\)-axis by a scale factor of \(\frac12\);
4. A reflection in the \(y\)-axis.

The equation of the resulting curve is \(y=\ln(2-4x)-2\).

Determine the equation of function \(\mathrm{f}\), showing your workings clearly.[4]