Domain and Range

Functions

Basic Conceptions

Cartesian Coordinate System

Domain and Range

Inverse Functions

Even-Odd Symmetry of Functions

Periodicity of Functions

Exponential and Logarithmic Functions

Exponential Functions

Logarithmic Functions
Natural Logarithms

Sets and Intervals

Hyperbolic Functions

Domain and Range

Key Topics Remaining: Inverse Functions » Even-Odd Symmetry of Functions » Exponential Functions » Logarithmic Functions » Natural Logarithms

Let x and y be two variables, and let D and R be sets of values of x and y, respectively.
If each value of x is associated with one value of y by some rule, then it is said that a function y of x is defined on the set D .
This statement is symbolized by the equation

y = f ( x ),

which is known as the function notation.

The indepentent variable x is also called the argument of y
The set D is called the domain of definition, and the set R is called the range of the function.

A function f is said to map the set D onto R if for every y in R there exists some x in D such that f ( x ) = y.

A function f is said to be an one-to-one relation, if the equality

f ( a ) = f ( b )

implies

a = b.

The equation y = f ( x ) can be interpreted graphically as an equation of a line in the x,y-plane.
A graphical representation allows to see an equation through a graph that is very helpful for finding the solutions.