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To determine the intervals on which the graph of \( f \) is decreasing, we need to identify where the slope of the graph is negative. In other words, the graph should be going down as we move from left to right.

Looking at the graph, \( f \) is decreasing when the curve is sloping downward. Specifically:

1. The graph decreases from \( x \approx -7 \) to \( x = -3 \), as the curve is moving downward.
2. The graph decreases again from \( x \approx 6 \) to \( x = 9 \), where the slope is negative.

Thus, the intervals where the graph of \( f \) is decreasing are approximately:
- \( (-7, -3) \)
- \( (6, 9) \)

Would you like further clarification or details on this?

Here are 5 related questions to further explore:
1. How do we determine intervals of increase for the same function?
2. What is the role of the first derivative in determining increasing or decreasing intervals?
3. How can critical points help in finding intervals of decrease?
4. What is the difference between local maximums and local minimums on a graph?
5. Can you explain how concavity affects the shape of the graph?

**Tip:** A graph is decreasing where the derivative is negative, meaning the slope of the tangent line at any point is negative.

Determine all intervals on which the graph of f is decreasing.

This page provides a solution to determining the intervals on which the graph of the function f is decreasing. Using visual analysis, we explore the intervals where the function has a negative slope, specifically from x ≈ -7 to x = -3 and x ≈ 6 to x = 9. Ideal for high school students in Grades 10-12.

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