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.

Learn how to graph the equation y = 4 - f(2x) with detailed steps, including horizontal compression, reflection, and vertical shifts. This problem introduces key function transformations and their effects on the graph, suitable for students in Grades 9-12.

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