Given a function f: AB, we say that f is **growing** in some set A 'A if and only if for any x_{1} The ex_{2} A ', with x_{1}<>_{2}, we have f (x_{1})<>_{2}).

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

x_{1}<>_{2} => x_{1}+1<>_{2}+1 => f (x_{1})<>_{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 x_{1} The ex_{2} A ', with x_{1}<>_{2}, we have f (x_{1})> f (x_{2}).

For example, the function f: IRIR defined by f (x) = - x + 1 is decreasing in IR because:

x_{1}<>_{2} => -x_{1}> -x_{2} => -x_{1}+1> -x_{2}+1 => f (x_{1})> f (x_{2}).

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.