To determine where \( f(x) \) is decreasing, we need to look at the slope of the function, represented by its derivative \( f'(x) \). A function is decreasing in regions where \( f'(x) < 0 \).

From the graph:

1. Identify intervals where the slope of \( f(x) \) is negative.
2. Visually inspect where the curve moves downward as \( x \) increases.

Based on the image provided, it appears that:
- \( f(x) \) is decreasing in the interval \(( -\infty, -1)\), where the function descends as \( x \) progresses from left to right.
- \( f(x) \) starts to increase again after \( x = -1 \).

So, the interval where \( f(x) \) is decreasing is approximately:
\[
(-\infty, -1)
\]

Would you like further details or have any other questions about this?

Here are five related questions you might find useful:
1. How do you determine intervals of increase for \( f(x) \)?
2. How can the derivative test be used to confirm intervals of increase or decrease?
3. What happens to \( f(x) \) at critical points where \( f'(x) = 0 \)?
4. How do concavity and inflection points affect the graph of \( f(x) \)?
5. What does it mean if \( f(x) \) is constant on an interval?

**Tip:** When analyzing a function graph, look for the intervals where it slopes downwards to identify where it’s decreasing.

Explore how to find where a function f(x) is decreasing by analyzing its derivative f'(x). This solution provides a step-by-step approach to identifying intervals where the slope is negative, suitable for advanced calculus students in Grades 11-12.

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