Function

1. Polynomial Function

1.1. A function of the form P(x)=amxn+an−1xn−1+⋯+a1x+a0 where ‘n’ is a positive integer and an,an−1,⋯,a1,a0 are real numbers.

2. Linear Function

2.1. A polynomial function with degree ‘t’ is called a linear function.

3. Quadratic Function

3.1. A polynomial function with degree ‘2’ is called a quadratic function. The most general form of a quadratic equation is f(x)=ax2+bx+c.

4. Identity Function

4.1. Let f:A→B be a function then ‘f’ is called an identity function if f(x)=x,∀x∈A.

5. Constant Function

5.1. Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘f’ from ‘A’ to ‘B’ is called a constant function if and only if the range of ‘f’ is a singleton.

6. Algebraic Function

6.1. A function defined by an algebraic expression is called an algebraic function. e.g. f(x)=x2+3x+6.

7. Cubic Function

7.1. A polynomial function with degree ‘3’ is called a cubic function. The most general form of a cubic function is f(x)=ax3+bx2+cx+d.

8. Rational Function

8.1. A function R(x) defined by R(x)=P(x)Q(x), where both P(x)andQ(x) are polynomial functions is called a rational function.