Increasing and Decreasing Functions
Main Concept
You may already be familiar with the vertical line test (used to determine if a relation is a function). There is also a horizontal line test, which can be used to determine if a function is strictly increasing or decreasing, or not. Consider a function whose graph has no breaks on any interval in its domain. If for every horizontal line that intersects the graph of the function, there is at most one point of intersection, then the function is strictly increasing or strictly decreasing on each interval in its domain; otherwise the function is not.
Use your mouse to draw a function in the graph below, and the title of the graph will change to reflect the classification of the function (for example, "Strictly Increasing"). The horizontal line test will be illustrated by gray lines and the places where those lines intersect the relation. Click to clear the graph.
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