https://file.aiquickdraw.com/mathbot/file/172629109517829x3sjgt.jpg

The image shows a graph of a function and asks to identify the intervals where the function is increasing. The question is in Ukrainian, and it reads: "Вкажіть проміжки зростання функції" which translates to "Indicate the intervals of increase of the function."

To find the increasing intervals, we look for the regions where the function's graph is rising as we move from left to right.

### Analysis of the graph:
- The function decreases until it reaches a local minimum around \(x = -2\).
- From \(x = -2\) to approximately \(x = 1\), the function increases.
- Then the function decreases again after \(x = 1\).

Thus, the interval where the function is increasing is approximately \((-2, 1)\).

### Answer:
Among the options given, the correct interval of increase is \([ -2; 1 ]\), although that specific interval is not listed, the closest match is likely related.

Would you like further details or explanations?

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Here are some related questions to consider:
1. What is the definition of increasing and decreasing functions?
2. How do you find intervals of increase or decrease using the first derivative?
3. What is the significance of critical points in a graph?
4. How do you identify local maxima and minima on a graph?
5. What role does the derivative play in determining the behavior of a function?

**Tip:** When analyzing a graph, always check the slopes in different intervals; if the slope is positive, the function is increasing, and if negative, it is decreasing.

Вкажіть проміжки зростання функції. (Indicate the intervals of increase of the function.)

Analyze a function's graph to find intervals where the function is increasing. Suitable for students in grades 9-11, this problem involves core concepts of functions and graph analysis.

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