# Functions:

Some variables are related to each other.

“When variable x depends upon the variable y then the function will be x = f(y), here x is the function of variable y. this function shows the relationship between both of the variables.In economics there are many variables which related with each other in some manner."

## Types of Functions:

The types of the functions between variables are defined as follows:

#### 1. Explicit Function:

When a single variable completely depends upon the other variable then the function or relationship they make will be called as explicit function. E.g. Y = f(x).

#### 2. Implicit Function:

The function in which two variables depends on each other. By obtaining the value of one variable we can find the value of other one. E.g. x = 8+9y.

#### 3. Inverse Function:

The two explicit functions which are the part of a single implicit function will be known as inverse function. For example:x = 10/y or y = 10/x both are inverse functions of each other.

#### 4. Increasing Function:

If both dependent and independent functions moves along the same direction then the function will be known as increasing function. Or in other words we can say that the values are directly proportional to each other.

#### 5. Decreasing Function:

In this function the values of both of the variables moves in opposite direction. The values are inversely proportional to each other in this function.

#### 6. Single Valued Function:

Keeping in view the value of independent variable when a single value of a dependent variable is given, then it is called as single valued function. Linear equation is such type of function. For example:y = 3x - 5 etc.

#### 7. Multi Valued Function:

In this function more than one value of dependent variable is given while placing only one value of independent variable. For example: y = ± 2