https://file.aiquickdraw.com/mathbot/file/1727917620294jydogk0d.jpg

The graph shows a function that begins with a horizontal line along the x-axis (from \( x = -\infty \) to \( x = 0 \)) and then increases from \( x = 0 \) to positive infinity.

The function is **increasing** on the interval where the graph rises, which starts at \( x = 0 \). Hence, the interval on which the function is increasing is:

\[
(0, \infty)
\]

Would you like further details on this, or do you have any other questions?

Here are five related questions for further exploration:
1. What is the behavior of the function on the interval \( (-\infty, 0] \)?
2. What is the slope of the function in the increasing interval?
3. How would you describe the domain and range of this function?
4. Can you find the equation of this piecewise function?
5. What would happen to the graph if we reflected it over the y-axis?

**Tip:** To check if a function is increasing or decreasing, observe the slope (rate of change) of the graph. If it's positive, the function is increasing.

What interval is the function increasing?

Learn how to determine the interval where a function is increasing by analyzing a graph. The solution shows that the function increases on the interval (0, ∞). Suitable for students in Grades 6-8.

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