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The graph shows a function with its increasing and decreasing intervals. To determine where the function is increasing, we need to analyze the slope of the graph visually.

A function is increasing when its slope is positive (the graph moves upwards as we go from left to right). Based on the graph:

1. The function is increasing on the intervals:
   - From approximately \(x = -4.5\) to \(x = -1\), where the graph rises from left to right.
   - From \(x = 1\) onwards, where the graph again rises as we move right.

Therefore, the intervals where the function is increasing are approximately:
- \( (-4.5, -1) \)
- \( (1, \infty) \)

Would you like further details or have any questions about this?

Here are 5 related questions:
1. How do you find decreasing intervals on a graph?
2. What are local maxima and minima on a graph?
3. How can you determine intervals of concavity from a graph?
4. What role does the derivative play in finding increasing intervals?
5. How would you solve for critical points analytically?

**Tip:** The derivative of a function tells you the slope of the tangent line at any given point, and you can use it to precisely find increasing and decreasing intervals.

In which interval is the function defined by the graph shown below increasing?

Explore how to find the intervals where a function is increasing by analyzing the graph. Understand key concepts from calculus, including the first derivative test, to identify when a graph rises from left to right. Suitable for Grades 10-12 students.

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