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The problem is asking to explain how to obtain the graphs of the given transformations of \( f(x) \). Here's a detailed explanation of how to handle each transformation:

1. **(a) \( f(x - 13) \):**
   - This is a horizontal shift to the right by 13 units.
   - The graph of \( f(x) \) moves rightward along the x-axis by 13 units.

2. **(b) \( 2f(x) - 13 \):**
   - The \( 2f(x) \) is a vertical stretch by a factor of 2, which makes the graph taller (doubles the y-values).
   - The \( -13 \) shifts the graph downward by 13 units.

3. **(c) \( 2f(x - 13) \):**
   - First, shift the graph of \( f(x) \) to the right by 13 units (horizontal shift).
   - Then apply a vertical stretch by multiplying the y-values by 2.

4. **(d) \( -4f(x + 13) \):**
   - Shift the graph of \( f(x) \) to the left by 13 units.
   - Then multiply the y-values by -4. This does two things: flips the graph over the x-axis (because of the negative sign) and stretches it vertically by a factor of 4.

5. **(e) \( f(x) + 1 \):**
   - This is a vertical shift upward by 1 unit.
   - The graph of \( f(x) \) moves upward along the y-axis.

6. **(f) \( -f(x/10) \):**
   - The \( x/10 \) means a horizontal stretch by a factor of 10.
   - The negative sign flips the graph of \( f(x) \) over the x-axis.

7. **(g) \( f(-x)/4 \):**
   - First, reflect the graph over the y-axis (due to the \( -x \)).
   - Then apply a vertical compression by dividing the y-values by 4.

8. **(h) \( -4f(-x) \):**
   - Reflect the graph over the y-axis.
   - Then apply a vertical stretch by a factor of 4 and flip it over the x-axis due to the negative sign.

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Do you have any questions, or would you like more detailed explanations on any specific transformation? Here are some related questions for further practice:

1. What happens if you replace \( f(x) \) with \( f(2x) \)?
2. How would you describe the transformation for \( f(x + a) + b \)?
3. What effect does multiplying \( f(x) \) by a negative constant have on the graph?
4. Can you explain the difference between horizontal and vertical shifts?
5. How would you graph \( f(-x - 5) + 3 \)?

**Tip:** For horizontal shifts, think in terms of the opposite sign (e.g., \( f(x - 3) \) shifts to the right).

Given is the graph of f(x). Explain (in words) how to obtain the graph of various transformations like f(x - 13), 2f(x) - 13, etc.

Learn how to apply transformations to functions, including horizontal shifts, vertical stretches, and reflections. This detailed explanation covers how to obtain the graph of transformations like f(x - 13), 2f(x) - 13, and more.

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