https://file.aiquickdraw.com/mathbot/file/1726934414602li4d0sit.jpg

To answer the question based on the graph you've provided, we will break down the intervals where the function is increasing, decreasing, and constant. Here's a step-by-step analysis of the graph:

### 1. **Increasing Intervals:**
   The function is increasing when the slope of the graph is positive (i.e., the line is going upwards). Based on the graph:
   - The function increases between the points \((-2, -6)\) and \((4, 4)\). This is because the graph moves upwards as we go from left to right between these points.

   So, the function is **increasing** on the open interval:
   \[
   (-2, 4)
   \]

### 2. **Decreasing Intervals:**
   The function is decreasing when the slope of the graph is negative (i.e., the line is going downwards). Based on the graph:
   - The function decreases between the points \((-6, 9)\) and \((-2, -6)\), as the line slopes downward.

   Therefore, the function is **decreasing** on the interval:
   \[
   (-6, -2)
   \]

### 3. **Constant Intervals:**
   The function is constant when the graph is a horizontal line (i.e., the slope is zero). Based on the graph:
   - The function is constant between \((4, 4)\) and \((7, 4)\).

   So, the function is **constant** on the interval:
   \[
   (4, 7)
   \]

### Final Answer for Part (a):
The function is increasing over the open interval **\((-2, 4)\)**.

If you have more questions or want further clarification, feel free to ask!

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Here are five related questions you might explore:

1. What is the definition of an increasing function in calculus?
2. How can you tell from the graph whether a function is constant over an interval?
3. How would you describe a function that is decreasing over multiple intervals?
4. What is the difference between open and closed intervals when describing the behavior of functions?
5. How does the concept of slope relate to whether a function is increasing or decreasing?

**Tip:** When analyzing a function graphically, focus on the slope of the lines to determine if it's increasing, decreasing, or constant over specific intervals.

State the open intervals over which the function is (a) increasing, (b) decreasing, and (c) constant. Based on the graph provided.

Learn how to determine the intervals where a function is increasing, decreasing, or constant using a given graph. This problem covers core calculus concepts related to function analysis, suitable for students in Grades 9-12.

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