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The problem compares the functions \( f(x) = -3^{2x} - 4 \) and \( g(x) = -3^{2x} \), asking how their graphs differ.

### Key Observations:
- The function \( f(x) = -3^{2x} - 4 \) includes the term "-4," which represents a **vertical shift**.
- The function \( g(x) = -3^{2x} \) does not have this constant term.

### Shift Explanation:
- The "-4" in \( f(x) = -3^{2x} - 4 \) shifts the graph of \( g(x) \) **downward by 4 units**.
- A vertical shift by a constant \( c \) affects the graph by moving it up or down without affecting the horizontal positioning.

### Conclusion:
- The graph of \( f(x) \) is shifted 4 units **down** from the graph of \( g(x) \).

Thus, the correct answer is **C. The graph of \( f(x) \) is shifted four units down from the graph of \( g(x) \)**.

Would you like further details or explanations?

Here are some additional questions to expand the discussion:
1. How does adding a positive constant affect the vertical shift of a graph?
2. What happens to the shape of the graph when constants are added or subtracted?
3. How does a horizontal shift differ from a vertical shift in function graphs?
4. Can you describe how the transformation \( f(x) = g(x) - 4 \) looks graphically?
5. What other transformations (e.g., reflections, stretches) can occur besides shifts?

**Tip:** Vertical shifts move the graph up or down, depending on whether the constant is added or subtracted.

How does the graph of f(x) = -3^(2x) - 4 differ from the graph of g(x) = -3^(2x)?

Learn how the graph of f(x) = -3^(2x) - 4 differs from g(x) = -3^(2x) by understanding vertical shifts in exponential functions. This problem helps students in Grades 9-11 understand how adding or subtracting constants affects graph positioning.

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