Answer:
- decreasing: (-4, 0) U (2, 4)
- increasing: (0, 2)
Explanation:
You want to identify intervals where the graph is increasing and where it is decreasing.
Up/Down
A graph is "increasing" if it is going up as you go from left to right on the graph. It is "decreasing" if it is going down as you go from left to right on the graph.
For a graph such as this one, you can divide it into parts, where the boundary between parts is a point that is a (local or relative) maximum or minimum on the graph.
High points
The high points on this graph are at x=-4 and x=2. The graph is increasing in the intervals leading up to the high points.
Low points
The low points on this graph are at x=0 and x=4. The graph is decreasing on the intervals leading up to the low points.
Increasing/Decreasing
The direction (increasing, decreasing) are indicated by green and magenta arrows, respectively. The interval boundaries are marked by blue lines.
- decreasing: (-4, 0) U (2, 4)
- increasing: (0, 2)
We use round parentheses ( ) to designate the intervals, because the flat spots and turning points are not included in the intervals of increase or decrease.
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Additional comment
When we say "leading up to" the turning point, we mean as you follow the graph from left to right. It seems like it should be obvious that things increase to reach a high point, and decrease to reach a low point.
You can write the first decreasing interval as an inequality:
-4 < x < 0
This is written in "interval notation" with the lower limit of the interval on the left: (-4, 0).
If the endpoint of an interval is included in the interval, the bracket used is a square bracket:
-6 ≤ x < 5 ⇔ [-6, 5)