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increasing vs. decreasing & pos vs. neg (level 2)

To determine where the function \( f \) is decreasing, we need to identify the intervals on the \( x \)-axis where the graph is sloping downwards as \( x \) increases.

Looking at the graph, \( f \) appears to be decreasing in the following intervals:
1. From \( x = -7 \) to \( x = -4 \), the graph slopes downward.
2. From \( x = -1 \) to \( x = 2 \), the graph also decreases.

Therefore, the intervals where the function \( f \) is decreasing are:
\[
(-7, -4) \text{ and } (-1, 2)
\]

Would you like further explanation on how to interpret these intervals or any other aspect?

Here are 5 related questions for further practice:
1. How do you determine where a function is increasing on a graph?
2. What is the significance of turning points in identifying increasing and decreasing intervals?
3. How can you identify intervals of positive and negative values for \( f(x) \)?
4. How does the concept of the derivative relate to increasing and decreasing intervals?
5. What is the role of concavity in understanding the behavior of a function's graph?

**Tip:** When analyzing graphs for increasing or decreasing behavior, always look for the slopes of the curve between critical points.

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

Learn how to determine intervals where a function is decreasing by analyzing the graph of f. This problem focuses on identifying sections of the x-axis where the graph slopes downward as x increases. Suitable for high school students in Grades 10-12.

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