https://file.aiquickdraw.com/mathbot/file/17270239997925oychqal.jpg

Looking at the graph in your image, we need to answer the following:

1. **(a) Increasing**: The function appears to increase on the interval where the graph is rising. From the graph, there are no clear portions where the graph is increasing. The segments either decrease or remain constant.

2. **(b) Constant**: The function is constant where the graph shows a horizontal line. In this case, the function remains constant from \( x = -2 \) to \( x = 2 \), as the graph is a flat horizontal line at \( y = 0 \) between these values.

3. **(c) Decreasing**: The function is decreasing where the graph falls. The function decreases on two intervals:
   - From \( x = -8 \) to \( x = -2 \)
   - From \( x = 2 \) to \( x = 6 \)

4. **(d) Domain**: The domain is the set of all \( x \)-values over which the function is defined. From the graph, the function is defined from \( x = -8 \) to \( x = 6 \). Therefore, the domain is:
   \[
   \text{Domain} = [-8, 6]
   \]

5. **(e) Range**: The range is the set of all \( y \)-values that the function takes. From the graph, the function goes from \( y = -4 \) to \( y = 0 \). Therefore, the range is:
   \[
   \text{Range} = [-4, 0]
   \]

Would you like further clarification on any of these points?

Here are 5 related questions to deepen your understanding:

1. How do you identify intervals of increase and decrease on a graph?
2. What are the criteria for determining the domain and range of more complex functions?
3. How would the domain and range change if the graph extended beyond the given interval?
4. Can a function have multiple intervals where it is constant, increasing, or decreasing?
5. What happens to the domain and range when the function has open or closed circles at the endpoints?

**Tip**: Always look for open or closed circles on the graph to determine if the endpoints are included in the domain or range!

Determine where the function is increasing, decreasing, or constant based on the graph, and find the domain and range.

This problem involves analyzing a function based on its graph to determine intervals where the function is increasing, decreasing, or constant. Additionally, the domain and range of the function are calculated. Suitable for students in Grades 9-11.

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