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Ascending function and decreasing function


Given a function f: AB, we say that f is growing in some set A 'A if and only if for any x1 The ex2 A ', with x1<>2, we have f (x1)<>2).

For example, the function f: IRIR defined by f (x) = x + 1 is increasing in IR because:
x1<>2 => x1+1<>2+1 => f (x1)<>2)

That is: as domain values ​​grow, so do your images.

On the other hand, given a function f: AB, we say that f is descending in some set A ' A if and only if for any x1 The ex2 A ', with x1<>2, we have f (x1)> f (x2).

For example, the function f: IRIR defined by f (x) = - x + 1 is decreasing in IR because:
x1<>2 => -x1> -x2 => -x1+1> -x2+1 => f (x1)> f (x2).

That is: when the domain values ​​grow, their corresponding images decrease. Examples:


This is an example of increasing function. We can see from the graph that as x values ​​increase, so do your images.


This is an example of descending function. We can see from the graph that as x values ​​increase, your images decrease.

Next: Composite Function