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To determine on what open intervals the function \( g(x) \) is decreasing from the graph, we need to look for the sections where the graph has a negative slope (i.e., where the graph is sloping downwards).

From the graph:

1. The function decreases between two specific points:
   - Between the peak at point \( A \) (approximately \( x = -2 \)) and the trough at point \( B \) (approximately \( x = 1 \)).
   - This gives the interval where \( g(x) \) is decreasing as \( (-2, 1) \).

So, the function is decreasing on the interval:

\[
(-2, 1)
\]

Would you like further details or have any questions on this? Here are 5 related questions to expand your understanding:

1. What is the definition of an increasing interval on a graph?
2. How can the first derivative help identify increasing and decreasing intervals?
3. How would you find the local minima and maxima of \( g(x) \)?
4. How do concavity and points of inflection relate to increasing and decreasing behavior?
5. How does this information about decreasing intervals help in understanding the overall behavior of a function?

**Tip**: To confirm decreasing intervals algebraically, the derivative \( g'(x) \) should be negative within those intervals.

On what open intervals is g(x) decreasing based on the graph?

Learn how to identify the intervals where the function g(x) is decreasing by analyzing its graph. This involves understanding the concept of slopes and using the first derivative test. Suitable for students in Grades 10-12.

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