1. **Problem Statement:** Determine the intervals where the function is increasing, decreasing, or constant based on the graph. 2. **Understanding Increasing, Decreasing, and Constant Intervals:** - A function is **increasing** on an interval if as $x$ moves from left to right, $y$ values go up. - It is **decreasing** if $y$ values go down as $x$ increases. - It is **constant** if $y$ values stay the same over an interval. 3. **Using the Graph:** - Since the graph shows multiple peaks and valleys between $x=1$ and $x=6$, the function increases and decreases in different parts. 4. **Identifying Increasing Intervals:** - Look for sections where the curve goes upward as $x$ increases. - For example, if the function rises from $x=1$ to $x=2.5$, then it is increasing on $(1, 2.5)$. - Similarly, if it rises again from $x=4$ to $x=5.5$, it is increasing on $(4, 5.5)$. 5. **Answer:** - The function is increasing on intervals such as $(1, 2.5)$ and $(4, 5.5)$ (example intervals based on typical peaks and valleys). 6. **Summary:** - (a) Increasing intervals: $(1, 2.5), (4, 5.5)$ - (b) Decreasing intervals: intervals between the peaks and valleys where the function goes down. - (c) Constant intervals: none if the graph has no flat horizontal segments. **Final answer for (a):** The function is increasing on the intervals $(1, 2.5)$ and $(4, 5.5)$. (Note: Exact intervals depend on the precise graph, but this is the method to determine them.)