Determine the intervals that a graph is increasing and decreasing

The video tutorial explains how to analyze graphs by identifying increasing and decreasing intervals. It covers the use of interval notation to denote included and excluded values, emphasizing the importance of parentheses. The tutorial also discusses local and relative minima and maxima, explaining how to identify these points within given intervals. The concept of absolute extrema is addressed, noting that they do not exist for graphs extending infinitely.

What does it mean for a graph to be increasing as we move from left to right?

• The x-values decrease as y-values increase.

• The y-values increase as x-values increase.

• The y-values remain constant as x-values increase.

• The y-values decrease as x-values increase.

How do you denote an interval where a value is included?

• Using parentheses ()

• Using angle brackets <>

• Using brackets []

• Using curly braces {}

What is the significance of using parentheses in interval notation?

• They indicate that the interval is finite.

• They indicate that the interval is infinite.

• They indicate that the endpoint is included.

• They indicate that the endpoint is excluded.

Why are there no absolute extrema in graphs that extend infinitely?

• Because the graph is always increasing.

• Because the graph is always decreasing.

• Because the graph has multiple highest and lowest points.

• Because the graph never reaches a highest or lowest point.

What defines a relative maximum in a given interval?

• A point that is neither the highest nor the lowest.

• The highest point in the entire graph.

• The highest point within a specific interval.

• The lowest point within a specific interval.