The image presents a graph of a piecewise function, and the question asks for the increasing intervals.

To determine the increasing intervals of a function:

• A function is increasing when, as the x-values increase, the y-values also increase.

Step-by-step analysis:

1. The graph appears to start decreasing until it reaches a minimum point at $x = 3$.
2. After this minimum point at $x = 3$, the graph increases from $x = 3$ to $x = 8$.
3. After $x = 8$, the function appears to remain constant.

Thus, the increasing interval is from $x = 3$ to $x = 8$, which corresponds to the option (4, 8).

Final Answer:

The correct increasing interval is $(4, 8)$.

Do you have any questions, or would you like more details?

5 Related Questions:

1. How do we determine decreasing intervals on a graph?
2. What is the significance of a constant interval in a function?
3. Can a function have multiple increasing intervals?
4. How do we find the maximum and minimum points on a graph?
5. What are the applications of analyzing increasing and decreasing intervals?

Tip:

Always check for sharp turns or peaks on a graph, as these points often separate increasing and decreasing intervals!