Increasing functions, decreasing functions

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

  1. 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
  2. The sum of several growing on this set of functions is an increasing function on this set.
  3. If the function is increasing, then reverse to it function also increases.
  4. 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.
  5. The result of consecutive application of increasing and decreasing functions a function is decreasing.
  6. Growing on any given set the function of each acquires its value only in one point from this set.
  7. — 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

  1. If the function spadano a lot , the more the value of the function corresponds to the least value of the argument from this set
  2. The amount of multiple descending on this set of functions is a decreasing function on this set.
  3. If the function is decreasing, then the reverse to it function also decreases.
  4. 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.
  5. The result of consecutive application of increasing and decreasing functions a function is decreasing.
  6. Descending on any given set the function of each acquires its value only in one point from this set.
  7. — 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

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