Increasing function
Definition: a Function 
is called increasing on some set 
if a greater argument value from this set corresponds to the greater value of the function.
— increasing, if for any 
Properties an increasing function of
- If the function
is increasing on some set 
, the greater the value of the function there corresponds a large value of the argument from this set - The sum of several growing on this set of functions is an increasing function on this set.
- If the function is increasing, then reverse to it function also increases.
- If the composed function
a function 
increases the function 
increases, the function increases. The result of successive application of two increasing functions is an increasing function. - The result of consecutive application of increasing and decreasing functions a function is decreasing.
- Growing on any given set the function of each acquires its value only in one point from this set.
a function 
increases the function 
increases, the function 
— increasing function
— increasing function
A sign of increasing functions
If 
at each point of the interval 
, the function is increasing on this interval.
Examples of functions are increasing in all scope
Descending function
Definition: a Function is called decreasing on some set if a greater argument value from this set corresponds to the greater value of the function.
— if for any
The properties of a decreasing function
- If the function spadano a lot , the more the value of the function corresponds to the least value of the argument from this set
- The amount of multiple descending on this set of functions is a decreasing function on this set.
- If the function is decreasing, then the reverse to it function also decreases.
- If the composed function is the function decreasing and the function is decreasing, then the function decreases. The result of successive application of two decreasing functions is an increasing function.
- The result of consecutive application of increasing and decreasing functions a function is decreasing.
- Descending on any given set the function of each acquires its value only in one point from this set.
— decreasing function
— decreasing function
Signs of decreasing function
If 
at each point of the interval , the function is decreasing on this interval.
Examples of features falling at the entire scope
