The transformation that converts the graph of $f(x) = -5|x+2| + 9$ into the graph of $g(x) = -5|x-2| + 9$ is a horizontal translation.

Specifically, the graph is translated 4 units to the right.

Explanation:

• The function $f(x) = -5|x+2| + 9$ has the term $|x+2|$, which means the graph of $f(x)$ is a reflection of the basic absolute value function $|x|$ and then shifted 2 units to the left.
• The function $g(x) = -5|x-2| + 9$ has the term $|x-2|$, which means the graph of $g(x)$ is a reflection of the basic absolute value function $|x|$ and then shifted 2 units to the right.
• To move from $f(x)$ to $g(x)$, the graph must be shifted 4 units to the right (from $x = -2$ to $x = 2$).

Would you like to see more details or have any questions about this transformation?

Here are 5 related questions:

1. How would you describe the effect of the coefficient $-5$ on the graph of $f(x)$?
2. What happens to the graph if you change the constant $+9$ to $+12$?
3. How would the graph change if $f(x) = -5|x+2|$ was modified to $f(x) = -3|x+2|$?
4. What is the vertex of the graph of $f(x)$ and $g(x)$?
5. How does the graph of $f(x)$ compare to the graph of $f(x) = |x+2|$?

Tip: Horizontal shifts are always in the opposite direction of the sign inside the absolute value.