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.