# List of Notes - Category: Function Types

## Increasing and Decreasing Functions

A function f is called increasing on interval I if f(x_1)<f(x_2) whenever x_1<x_2 in I.

A function f is called decreasing on interval I if f(x_1)>f(x_2) whenever x_1>x_2 in I.

## Even Odd Function

If f(x)=f(-x) for every x in the domain of f then f is an even function.

For example, f(x)=x^2 is even because for every x f(-x)=(-x)^2=x^2=f(x).

If f(-x)=-f(x) for every x in the domain of f then f is an odd function.

## Piecewise Function

When functions is determined by different formulas on different intervals then function is piecewise.

For example, f(x)={(1-x if x<0),(x^2 if x>=0):} is piecewise because on interval (-oo,0) f(x)=1-x and on interval [0,oo) f(x)=x^2.

## Periodic Function

Function y=f(x) is called periodic if exists such number T!=0 that for any x from domain of the function f(x+T)=f(x).

From the definition it follows that periodic function has infinitely many periods. If T is period of function then any number of the form kT, where k is integer,is also period of function.