1. The problem is to understand the transformation represented by the equation $2y = f(x) - 4$. 2. Start by isolating $y$ to express it in terms of $f(x)$: $$2y = f(x) - 4$$ Divide both sides by 2: $$y = \frac{f(x) - 4}{2} = \frac{f(x)}{2} - 2$$ 3. This shows two transformations applied to the function $f(x)$: - The output of $f(x)$ is first shifted down by 4 units (subtracting 4). - Then the entire expression is scaled by a factor of $\frac{1}{2}$ (dividing by 2), which compresses the graph vertically by a factor of 2. 4. In summary, the transformation $2y = f(x) - 4$ corresponds to: - A vertical shift downward by 4 units. - A vertical compression by a factor of 2. 5. If you want to graph this, you would take the graph of $f(x)$, shift it down 4 units, then compress it vertically by half. Final transformed function: $$y = \frac{f(x)}{2} - 2$$