The transformation that converts the graph of $f(x) = 5|x + 5| - 8$ into the graph of $g(x) = 5|x - 5| - 8$ is a horizontal translation.

Specifically, this is a shift of the graph of $f(x)$ 10 units to the right to obtain the graph of $g(x)$.

Explanation:

1. The function $f(x) = 5|x + 5| - 8$ has a vertex at $(-5, -8)$.
2. The function $g(x) = 5|x - 5| - 8$ has a vertex at $(5, -8)$.
3. To transform $f(x)$ into $g(x)$, you need to move the graph from the vertex at $(-5, -8)$ to the vertex at $(5, -8)$.
4. This movement is achieved by shifting the graph 10 units to the right.

The other components of the function (the coefficient of 5 and the constant term -8) remain unchanged, indicating that there is no vertical shift, stretch, or compression involved—just the horizontal translation.

Would you like a detailed graphical representation or have any questions?

Here are some related questions to explore:

1. What effect does changing the coefficient of $|x|$ have on the graph of an absolute value function?
2. How would you translate $f(x) = 5|x + 5| - 8$ vertically to match $g(x) = 5|x - 5| - 3$?
3. What happens to the graph of an absolute value function when you reflect it over the y-axis?
4. How do you find the vertex of a function in the form $f(x) = a|x - h| + k$?
5. How does shifting the graph horizontally affect the domain and range of an absolute value function?

Tip: When analyzing transformations, always identify changes to the $x$- and $y$-values separately to determine horizontal and vertical shifts, reflections, stretches, and compressions.