https://file.aiquickdraw.com/mathbot/file/1726288601427a0wfx1bm.jpg

To determine the intervals where the function in the graph is increasing, we need to observe where the slope of the graph is positive—that is, where the graph moves upwards as we move from left to right.

From the graph, we can see the following:

1. The function decreases initially until it reaches a local minimum.
2. The function starts increasing from approximately \( x = -6 \) to \( x = 2 \).
3. After reaching \( x = 2 \), the function starts decreasing again.

Thus, the function is increasing on the interval:
\[
(-6, 2)
\]

Would you like any further details or explanations?

Here are 5 related questions you might find interesting:
1. How can we identify decreasing intervals on the same graph?
2. How do we find the points where the slope changes sign (turning points)?
3. What role do critical points play in determining increasing and decreasing intervals?
4. How would you determine whether a function is concave up or concave down from a graph?
5. What methods can we use to determine increasing/decreasing intervals algebraically?

**Tip:** When analyzing graphs, always pay close attention to changes in the slope to identify intervals of increase and decrease.

Over what interval is the function in this graph increasing?

Learn how to identify the increasing interval of a function by analyzing its graph. This example focuses on determining the interval where the graph's slope is positive, specifically from x = -6 to x = 2. Suitable for students in Grades 9-10.

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