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The question provided is written in Persian and includes a mathematical expression. I'll translate and interpret it to guide you through the solution.

Translation:
- The problem gives the point \( A(1, -4) \) on the graph of the function \( y = 3 - f(x) \). It asks you to determine the coordinates of point \( A \) on the graph of the function \( y = f(x - 2) \).

### Step-by-Step Solution:
1. **Initial Function**: The given function is \( y = 3 - f(x) \), and point \( A(1, -4) \) lies on this curve.
   - This means that for \( x = 1 \), \( y = -4 \).
   - So, we substitute \( x = 1 \) and \( y = -4 \) into the equation \( y = 3 - f(x) \):
     \[
     -4 = 3 - f(1)
     \]
     Solving for \( f(1) \):
     \[
     f(1) = 3 + 4 = 7
     \]
     Therefore, \( f(1) = 7 \).

2. **New Function**: The next part of the problem asks for the coordinates on the graph of the transformed function \( y = f(x - 2) \).
   - In this case, we have a horizontal shift of the function by 2 units to the right.
   - We know \( f(1) = 7 \), so now we are interested in the value of \( f(x-2) \) when \( x = 1 \).

3. **Finding \( f(x - 2) \)**: If \( f(1) = 7 \), and we are now dealing with \( f(x - 2) \), we substitute \( x = 3 \) (since \( x - 2 = 1 \)) into \( f(x - 2) \):
   - For \( x = 3 \), \( f(3 - 2) = f(1) = 7 \).

Thus, the coordinates on the new graph of \( y = f(x - 2) \) corresponding to point \( A(1, -4) \) are \( A(3, 7) \).

Would you like more details or have any further questions?

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Here are 5 related questions to extend this concept:
1. What is the effect of a vertical shift on the graph of \( f(x) \)?
2. How do horizontal shifts affect the domain of a function?
3. What happens to the graph of \( f(x) \) if you apply both vertical and horizontal shifts?
4. Can we find the inverse of \( f(x) \), and how does the graph change?
5. What are the coordinates of point \( A \) if the function is transformed to \( f(2x) \)?

**Tip**: Always check how transformations like horizontal shifts impact the input variable \( x \) when applying them to functions.

A point A(1, -4) lies on the graph of the function y = 3 - f(x). Determine the coordinates of point A on the graph of the transformed function y = f(x - 2).

Find the coordinates of a point on a transformed function graph. Learn how to solve this problem involving horizontal shifts and function transformations using y = f(x - 2). Suitable for high school students.

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