Afunction f is on an open interval i if, for any choice of x1 and x2 in i, with 1 less than

If whenever f is increasing on I.

If whenever f is decreasing on I.

Step-by-step explanation:

These are definitions for real-valued functions f:I→R. To help you remember the definitions, you can interpret them in the following way:

When you choose any two numbers on I and compare their image under f, the following can happen.

Note that this must hold for ALL choices of x1, x2. There exist many functions that are neither increasing nor decreasing, but usually some definition applies for continuous functions on a small enough interval I.