## Concept of Mathematics

Function

**The function** is a relation that associates each element x of a set X, the domain of the **function**, to a single element y of another set Y the **function**.

**The various types of functions are as follows: **Many to one **function**.

One-to-one **function**.

Onto **function**.

One and onto **function**.

Constant **function**.

Identity **function**.

Quadratic **function**.

Polynomial **function**.

## One to one **function**.

A function is one to one if no two elements in the domain of g correspond to the same element in the range of g.

In other words, each u in the domain has exactly one image in the range.

And, no v in the range is the image of more than one u in the domain.

## Onto **function**.

**Onto function can be explained by considering two sets, Set X and Set Y,**

**which consist of some elements not empty. If for every element of Y,**

**there is at least one or more than one element mapping with X,**

**then the function is called onto function or surjective function.**

## Constant **function**.

**A constant function is a linear function whose range contains only one element of a domain.**

## Identity **function**.

The function f is called the identity function if every element of set X has an image on itself.

## Quadratic **function**.

**Quadratic function** is written in the form f(x) = ax^{2} + bx + c,

where a, b, and c are coefficient with a not equal to zero.

The graph of a **quadratic function** is a curve called a parabola.

## Polynomial **function**.

A **polynomial function** is a **function** that consists of only non-negative integer powers

or only positive integer exponents of a variable in an equation is called a quadratic equation.

## **Sequence and series**

**Sequence**

A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If b_{1}, b_{2}, b_{3}, b_{4},………

**Types of Sequences**

Arithmetic **Sequence**.

An arithmetic sequence is a sequence of numbers that the difference of any two consective members of the sequence is a constant.

2,4,6,8,10….is an arithmetic sequence with have same common diff.

an=a1+(n−1)d is the formula of arithmetic sequence a1 is called 1st term and d is called common difference.

Sn=n2(a1+an) is the formula of the sum of the arithmetic sequence where a1 is 1st and a^n is called last term of the sequence.

Geometric **Sequence**.

A geometric **Sequence**. is a sequence that have the same common ratio is defined as that

if the division of any two consecutive no is always the same for example 2,4,8,16…..

for example 4/2=2 and 8/4=2

Harmonic **Sequence**.

the harmonic sequence is reciprocal of an arithmetic sequence, for example, 1/a,1/b,1/c..

**The nth term of the Harmonic Progression (H.P) = 1/ [a+(n-1)d]**

Where

a is the first term of A.P

d is the common difference

n is the number of terms in A.P