Increasing and Decreasing Intervals

Description/Explanation/Highlights

Video Description of Increasing and Decreasing Intervals

This video explains how to identify increasing, decreasing, as well as constant intervals on a graph.

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Steps and Key Points to Remember to Determine Increasing and Decreasing Intervals

To determine intervals of a graph, follow these steps:

  1. Intervals on a graph refer to the parts of the graph that are moving up, down, or staying flat as the graph is read from left to right.
  2. As the value of x increases, increasing intervals occur when the values of y are also increasing.
  3. Decreasing intervals occur when the values of y are decreasing.
  4. Constant intervals occur when the y-values stay the same as x-values increase.
increasing and decreasing intervals graph 1
  1. In the graph above, the graph increases over the part that is drawn in red.
  2. The graph stays constant on the blue line.
  3. It decreases on the black part.
  4. First, the graph increases on the interval from negative infinity to -4.
  5. Secondly, the graph is constant on the interval from -4 to 3.
  6. Thirdly, the graph decreases on the interval from 3 to positive infinity.
increasing and decreasing intervals graph 2
  1. To identify the intervals in the graph above, look from left to right. Notice that there are no y-values defined for x until x reaches -7.
  2. The y-values get larger until x reaches -5. This is an increasing interval.
  3. Notice that the y-values also increase from 2 to positive infinity. Note the arrow on the right end of the graph on x. This is also an increasing interval.
  4. Write these increasing intervals in interval notation as: (-7, -5), (2, \(\infty\)).  Notice that we always use parenthesis and not brackets when writing intervals. The point where the graph changes direction is never increasing or decreasing. It is just a point!
  5. This graph only has one decreasing interval, from -5 to -2 on x which is written as (-5, -2).
  6. There is also a constant interval where the y-values are not changing. This occurs on the interval (-2, 2).

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Here are some key points to keep in mind when determining intervals on a continuous graph:

  • Always look at the graph from left to right when identifying intervals.
  • The intervals are identified by the x-values while looking at what y-values are doing as x-values increase.
  • All defined intervals on a continuous graph either increase, decrease, or stay constant.
  • Intervals are identified from the x-value of the point where y starts to increase, decrease, or stay constant, and by the x-value where the direction changes when observing left to right.
  • Usually, write identified intervals in interval notation.
  • When writing intervals in interval notation, always use parenthesis on both ends. This is because the x-value of the beginning and ending point is neither increasing nor decreasing.

Video Highlights

  • 00:00 Introduction
  • 00:15 Explanation of intervals
  • 00:32 Example graph with increasing, decreasing, and constant intervals
  • 01:49 Example of identifying intervals on a graph and writing in interval notation
  • 05:12 Conclusion

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