The following types of functions are known as algebraic function:

Algebraic functions are also known as Polynomial functions.

a. The Identity Function:

The function defined by y=f(x)=x is known as identity function.

For example:

If I:R→R is a  function defined by f(x)=x=y then the function “I” is a identity function.

We can show a identity function in graph as:

b. The Constant Function:

The function defined by y=f(x)=k , where “k” is a constant is known as constant function.

For example:

If A={1,2,3} and b={1} and f:A→B defined by y=f(x)=1 then “f” is a constant function.

We can show a constant function in graph as:

c. The Linear Function:

The function defined by y=f(x)=mx+c where “m” and “c” are constants is known as linear function.

For example:

If f:A→B is defined by y=f(x)=2x+1 then “f” is a linear function , where m=2 and c=1

We can show linear function in graph as:

d. The quadratic function:

The function defined by y=f(x)=ax²+bx+c is known as quadratic function where “a” , “b” and “c” are constants.

For example:

If f:A→B is defined by y=f(x)=x² then “f” is a quadratic function where a=1 and b=c=0

We can show quadratic function in graph as:

e. The cubic Function:

The function defined by y=f(x)=ax³+bx²+cx+d is known as cubic function.

For example:

If f:A→B is defined by y=f(x)=x³ then “f” is a cubic function where a=1 and b=c=d=0

We can show cubic function in graph as: