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The question shown in the image asks you to analyze the graph of a function to determine where the function is increasing, decreasing, or constant. Let's go through it step by step:

1. **Identifying intervals of increase**: 
   The graph shows a function that starts by decreasing and then increases. We need to identify the part where the function is increasing. From the graph, the increase occurs after \(x = 2\), where the slope is positive.

   Therefore, the function is increasing on the interval \( (2, \infty) \), which corresponds to option **C**.

2. **Identifying constant intervals**: 
   A function is constant when the graph is a horizontal line, meaning the function doesn't change its value. In this graph, the function is constant between \(x = -2\) and \(x = 2\), which is a flat part of the graph.

   Thus, the function is constant on the interval \( [-2, 2] \), which corresponds to option **D**.

Would you like more detailed steps or have any questions about the graph? 

Here are 5 related questions to expand on this concept:
1. What is the relationship between the derivative of a function and increasing/decreasing behavior?
2. Can a function have more than one interval where it is constant?
3. What does it mean for a function to be decreasing, and how can we identify that on a graph?
4. How can you determine the maximum or minimum points from a graph of a function?
5. What role do endpoints of intervals play when discussing increasing and decreasing intervals?

**Tip**: When analyzing a graph, always look for changes in slope to determine increasing or decreasing behavior.

From the graph of the function, state the intervals on which the function is increasing, decreasing, or constant.

Determine the intervals on which the function is increasing, decreasing, or constant by analyzing the graph. Learn how to interpret graphs and identify different behaviors of a function. Suitable for students in Grades 9-12.

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