To graph the equation $y = 4 - f(2x)$, the graph of the function $f(x)$ is transformed in the following ways:

1. Horizontal compression by a factor of 2: The input $2x$ means that the function is compressed horizontally by a factor of 2. Every point on the graph moves closer to the y-axis.

2. Reflection over the x-axis: The negative sign in front of $f(2x)$ reflects the function across the x-axis.

3. Vertical shift upwards by 4 units: The "+4" outside of the function shifts the graph upward by 4 units.

Steps to graph $y = 4 - f(2x)$:

• Start with the graph of $f(x)$.
• Apply the horizontal compression (multiply the x-values by 1/2).
• Reflect the graph over the x-axis (multiply the y-values by -1).
• Finally, shift the entire graph upward by 4 units.

If you'd like, you can specify what function $f(x)$ is to generate an exact graph.

Would you like further details or examples on how this transformation works?

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Here are 5 related questions:

1. How do horizontal stretches/compressions affect a graph?
2. What is the impact of a vertical shift on a function's graph?
3. How does reflecting a graph across the x-axis change the function?
4. Can you graph functions without specifying $f(x)$?
5. How can we combine multiple transformations into a single graph?

Tip: When graphing transformations, always apply horizontal transformations before vertical ones for clarity.