Step 1 :The transformation from \(f(x)\) to \(g(x)\) involves a change in the coefficient of \(x\). In \(f(x)\), the coefficient of \(x\) is 2, while in \(g(x)\), the coefficient of \(x\) is 4. This indicates a vertical stretch of the function \(f(x)\) by a factor of 2.
Step 2 :\(\boxed{\text{The transformation that occurred was a vertical stretch of } f(x) \text{ by a factor of 2}}\)