https://file.aiquickdraw.com/mathbot/file/1726272529064ewxbdyte.jpg

Use the graph to determine
a. open intervals on which the function is​ increasing, if any.
b. open intervals on which the function is​ decreasing, if any.
c. open intervals on which the function is​ constant, if any.

Looking at the provided graph of the curve, we can break down the intervals of increasing, decreasing, and constant behavior.

### a. Open intervals on which the function is increasing:
- The function increases as we move from the bottom-left of the graph toward the top-right. This occurs after the vertex, which is located at \(x = -2\).
- **Interval of increase**: \((-2, \infty)\)

### b. Open intervals on which the function is decreasing:
- The function decreases as we move from the left towards the vertex at \(x = -2\).
- **Interval of decrease**: \((-\infty, -2)\)

### c. Open intervals on which the function is constant:
- There are no intervals where the function remains constant, as the curve either increases or decreases throughout.

Let me know if you would like more detailed explanations or if you have any specific questions!

### 5 Related Questions:
1. How do you determine the vertex of a function based on its graph?
2. What is the significance of increasing and decreasing intervals in calculus?
3. How can you determine if a function is concave up or concave down from its graph?
4. What type of function does this graph likely represent (linear, quadratic, etc.)?
5. How can you determine the axis of symmetry for this graph?

### Tip:
When analyzing a graph, always start by identifying key points like the vertex, intercepts, and any symmetry before breaking down the behavior over intervals.

Use the graph to determine
a. open intervals on which the function is increasing, if any.
b. open intervals on which the function is decreasing, if any.
c. open intervals on which the function is constant, if any.

Learn how to determine the increasing, decreasing, and constant intervals of a function using its graph. This concept uses interval notation and applies to students in Grades 9-12 studying calculus and graph analysis.

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