To analyze the function’s behavior in terms of increasing, decreasing, and constant intervals, we need to observe the graph closely.
Increasing Intervals: The function is increasing where the graph slopes upward from left to right. To identify these intervals, look for sections where the y-values increase as x-values increase. For example, if the graph rises from x = a to x = b, we can conclude that the function is increasing on the interval (a, b).
Decreasing Intervals: Conversely, the function is decreasing where the graph slopes downward from left to right. Here, you should look for sections where the y-values decrease as x-values increase. For instance, if the graph falls from x = c to x = d, then the function is decreasing on the interval (c, d).
Constant Intervals: Lastly, the function is constant where the graph remains horizontal, indicating that the y-values do not change as x-values do. If the graph is flat between x = e and x = f, then the function is constant on the interval (e, f).
In summary, to determine the intervals of increasing, decreasing, and constant behavior, carefully examine the slopes of the graph at different segments. Mark down the specific points where the behavior changes to identify these intervals clearly.