# Types of Function | Different Types of Functions

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Hi friends, in today’s article we are going to know about the different types of function. So let’s discuss in details.

## What are the Types of Function?

Identity Function – If the change in the value of independent variable X leads to same change in the value of dependent variable Y. Then such functional relationship is called identity function, such as a function can be expressed as –

Y = f(x) = X

Graph of Identity Function – We can draw the graph of identity function. The graph of identity function will be straight line passing through the origin –

Let, Y = f(x) = X

Polynomial Function – A function is stated to be polynomial function while its range consists of more than one element. In other words, a function is said to be polynomial if the function takes the following form –

Y = f(x) = ao + a1x + a2x2 + a3x3 +…+ anxn

When, n is non-negative integer and ao, a1…an are co-efficient of independent variable X.

Polynomial function can be classified as –

(i) Constant Function

(ii) Linear Function

(iv) Cubic Function

Constant Function – A function is said to be constant function whose output value or range is same for every input value or domain. In other words, the polynomial function in which the power of independent variable is zero is called constant function.

So, the constant function can be written as – Y = f(x) = C

The graph of a constant function is a straight line parallel to X axis. When C>0 then the graph lies above the X axis. When C<0, it lies below the X axis. As for example – if Y =f(x) = 3 then its graph will be a straight line parallel to X axis as shown in the below diagram –

Linear Function – A polynomial function is said to be linear if the largest power of independent variable is one (1). The graph of linear function is always a straight line.

Y = f(x) = ao + a1x

Quadratic Function – A polynomial function is said to be quadratic function when the power of independent variable is two (2). This function can be expressed as –

Y = f(x) = ao + a1x + a2x2

The graph of quadratic function is ‘Parabola’ that is ‘U’ shaped.

Cubic Function – In a function when largest power of independent variable is three (3), then that the function is known as cubic function. It can be expressed as –

ao + a1x + a2x2 + a3x3

Or Y = X3

Rational Function – Rational function is that in which the dependent variable (Y) is expressed as a ratio of two polynomials in the independent variable (X). It can be expressed as –

Y = f(x) = bo + b1x/ bo + b1x1 + b2x2

Or Y = f(x)/h(x)

The graph of rational function is rectangular hyperbola.

#### Conclusion

So friends, this was the types of function in mathematics or economics. Hope you get the full details about it and hope you like this article.

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