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To determine the intervals where the graph of the function \( f(x) \) is increasing, we need to identify the sections of the graph where the slope is positive (i.e., where the graph is rising as we move from left to right).

Looking at the provided graph:

1. The function is increasing where the graph moves upward. This happens in the following intervals:
   - From \( x \approx -7.5 \) to \( x \approx -4 \) (the graph rises from left to right).
   - From \( x \approx -1 \) to \( x \approx 2.5 \).
   - From \( x \approx 5.5 \) onward, the graph starts increasing again and continues beyond \( x = 9 \) (since the graph is not fully shown, it suggests that the increase continues).

Thus, the intervals on which the graph of \( f(x) \) is increasing are approximately:
\[ (-7.5, -4), \ (-1, 2.5), \ (5.5, \infty) \]

### Would you like me to break down why these intervals are identified as increasing or provide more details on how to solve such problems?

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Here are 5 related questions you might consider next:
1. What are the intervals where the graph of \( f(x) \) is decreasing?
2. How do you find critical points where the function changes from increasing to decreasing?
3. Can you describe how to use the derivative to determine increasing and decreasing intervals?
4. What are the points of local maxima and minima in this graph?
5. How do concavity and inflection points relate to increasing and decreasing intervals?

**Tip:** To determine if a function is increasing or decreasing using calculus, compute the derivative \( f'(x) \). If \( f'(x) > 0 \), the function is increasing; if \( f'(x) < 0 \), it's decreasing.

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

Learn how to identify the increasing intervals on the graph of a function by analyzing where the slope is positive. This article covers essential concepts such as function behavior and slope analysis, suitable for high school students studying advanced algebra.

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