What kind of transformation converts the graph of f(x)=
–
5|x+2|+9 into the graph of g(x)=
–
5|x–2|+9?

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.

Explore how horizontal translation transforms absolute value functions. Learn the specific transformation that converts f(x) = -5|x+2| + 9 into g(x) = -5|x-2| + 9 through a detailed explanation and examples. Suitable for high school students studying functions and transformations.

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