Question - Identifying Function Increase and Decrease Intervals
Solution:
The image displays the graph of a function, and you are asked to determine the intervals where the function is increasing or decreasing.When a function is increasing, the y-values (the values on the vertical axis) get larger as the x-values (the values on the horizontal axis) increase. Conversely, a function is decreasing when the y-values get smaller as the x-values increase.Looking at the graph:- The function is increasing from approximately x=-4 to x=-2.5, x=-1 to x=0, and x=2 to x=3.- The function is decreasing from x=-5 to x=-4, x=-2.5 to x=-1, x=0 to x=2, and x=3 to the end of the graph at x=4.To describe these intervals, you can use interval notation, where you use parentheses to denote values that are not included in the interval (open interval) and square brackets for values that are included (closed interval).From the graph, it is not clear whether the extrema (the highest and lowest points along each interval) are included because we do not have precise points. However, since extrema are usually considered part of both increasing and decreasing intervals, if the interval is described using precise points, such points are typically included.Therefore, the intervals should be described as roughly:- Increasing: (-4, -2.5), (-1, 0), and (2, 3)- Decreasing: (-5, -4), (-2.5, -1), (0, 2), and (3, 4)If these values were precisely known from the graph, closed brackets would be used at the extrema. It is important to remember that the exact values may differ slightly, and it's often best to get these values from the context of the question or the accompanying material.
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