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The graph shows a function \( f \) for the interval \( -5 \leq x \leq 5 \). The question asks about the rate of change of \( f \) over the interval \( -4 \leq x \leq -1 \).

### Analyzing the graph:

1. **Interval \( -4 \leq x \leq -1 \):**
   - In this interval, the function is **increasing** since the slope of the curve is positive.
   - As \( x \) moves from \( -4 \) to \( -1 \), the function rises, meaning the rate of change (slope of the tangent) is positive.
   - The rate of change seems to be **decreasing** as \( x \) approaches \( -1 \) because the graph starts steep but flattens out.

### Conclusion:
- The **rate of change is positive**, but it is **decreasing** over this interval, as the slope becomes less steep towards \( x = -1 \).

Would you like further clarification on this or a breakdown of possible answer choices?

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Here are 5 related questions for deeper understanding:

1. What is the geometric meaning of the rate of change in a function's graph?
2. How can you determine if the rate of change is increasing or decreasing from a graph?
3. What does it mean if a function is increasing but the rate of change is decreasing?
4. How do you calculate the average rate of change over a given interval?
5. What role do inflection points play in analyzing changes in the rate of change?

**Tip:** When examining graphs, the steepness of the curve gives a clear indication of the rate of change.

Which of the following statements about the rate of change of f over the interval -4 ≤ x ≤ -1 is true?

Understand how to analyze the rate of change of a function f over the interval -4 ≤ x ≤ -1, using graph analysis. Learn about the slope of a curve and how to determine if the rate of change is increasing or decreasing. Suitable for students in Grades 11-12.

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