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The problem asks for the coordinates of a transformed point on the graph of the function \( y = f(2x - 4) \), where the point \( (4, -12) \) lies on the graph of \( y = f(x) \).

### Step-by-Step Solution:

1. **Given**: \( (4, -12) \) is on the graph of \( y = f(x) \). So, \( f(4) = -12 \).

2. **Transformation**: The transformation \( y = f(2x - 4) \) involves a **horizontal shift and stretch**:
   - **Shift**: The expression inside the function, \( 2x - 4 \), indicates a horizontal shift by 2 units (because \( x - 2 = 0 \) when \( 2x - 4 = 0 \)).
   - **Stretch**: The factor of 2 means the graph is horizontally compressed by a factor of \( \frac{1}{2} \).

3. **Find the new x-coordinate**: To map the original point \( (4, -12) \) onto the new function, we solve for \( x \) in \( 2x - 4 = 4 \) (since \( f(4) = -12 \)):
   \[
   2x - 4 = 4 \implies 2x = 8 \implies x = 4.
   \]
   So, the new x-coordinate is \( x = 6 \).

4. **y-coordinate remains the same**: Since \( f(4) = -12 \), the new y-coordinate for this point is still \( -12 \).

Therefore, the transformed point is \( (6, -24) \).

### Final Answer:
The correct transformed point is \( (6, -24) \).

Do you need further details or have any questions?

Here are five related questions for further practice:
1. What happens to a point \( (x, y) \) under the transformation \( y = f(3x - 6) \)?
2. If \( y = f(x + 2) \), how does the graph of \( f(x) \) shift?
3. How does the graph of \( f(x) \) change when transformed into \( y = f(-x) \)?
4. What is the effect of the transformation \( y = 2f(x) \) on the graph of \( f(x) \)?
5. How do you find the inverse of a horizontal stretch transformation?

**Tip**: Horizontal transformations are counterintuitive—they affect the graph by acting on the x-coordinate in the opposite way!

The point (4, -12) lies on the graph of y = f(x). What are the coordinates of the transformed point on the graph of the function y = f(2x - 4)?

Find the coordinates of the transformed point when the function y = f(x) undergoes the transformation y = f(2x - 4). Understand the effects of horizontal shifts and stretches on the graph. Suitable for students in Grades 10-12.

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