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.

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).