ppt

1. Function & Types Of Function
Name:-Aamir Zahoor
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2. Functions
The term ‘functions’ refers to the relationship between the variables. When change in one
variable is observed due to change in the other variable , then it is said to have functional
relationship. In other words , a variable `y’ is said to be a function of another variable `x’ when
to every value of `x’ there corresponds a definite value of `y’. It is written as
y = f (x)
Here `x’ is called ind.ependent variable and `y’ is called dependent variable
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3. Domain and Range of Function
The set of values which an independent variable can assume is called the domain of the function
and the set of corresponding values of y(i.e. dependent variable) is called the range of the
function. Functions are helpful to understand the relation among different Input and Output
variables of Business.
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4. Types of Functions Functions
Functions are classified into the following categories
 Explicit and Implicit Functions : -A function y f(x) is said to be an explicit function of x
if the value of y is directly given in terms of x. It is written as
y = f(x)
But if the variables y and x are mixed in the functional relationship, then the function is
said to be an implicit function It is written as
f(x,y) = 0
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5.  Increasing and Decreasing Functions:- A function (x) is said to be an increasing
function of x if the value of y always increases as x increases. The function (x) is said to
be a decreasing function of x if the value of y always decreases as the value of x
increases. Normal demand functions and total cost functions are decreasing and
increasing functions respectively.
 Even and Odd functions : -A function f(x) is said to be an even function of x if
f(-x)=f(x). e.g. (x) = X2is even function. Similarly a function f(x) is said to be an odd
function of x if f(-x)= -f(x).e.g. f(x) = x3is an odd function.
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6.  Polynomial Functions :-
A function of the form
Y = f(x) = a0 + A1 x +a2x2 + …………………….… anxn
where n is a positive integer and ,a1 ≠ 0 is called a polynomial function of degree n.
If n=0, we have y = f(x) = a , a constant function
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12. Thanku
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