Definition of increasing and decreasing functions :

A function is increasing on an open interval if for any and in , with , then .

A function is decreasing on an open interval if for any and in , with , then .

Examples for increasing and decreasing functions :

Increasing function graph:                                             Decreasing function graph:

For instance, function is .

Let in interval .

.

Since , the function is increasing in the interval .

Let in interval .

.

Since , the function is decreasing in the interval .

Graph:

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Increasing function graph:                                             Decreasing function graph: