**What is the Best Definition of Function in Math**

*A special type of relation is a ***function ***defined as below:*

- f is a relation from A to B that is, f is a subset of
**A × B**. - Dom
**f= A**. - First element of no two pairs of f are equal, then f is said to be a function from A to B.

**A function is also written as**

**f: A➝B.** Which is read: f is a function from** A** to** B.**

*Every function is a relation. but every relation is not a function*.

Define Function with Details In simple words

if **A** and **B** are two sets then relation** f: A➝B** is called a function if for every element of A there exists a unique integer in **B** and Dom **f=A**. its main identification is When the domain does not repeat, it is a function.

**What is the Best** **Examples of a Function**

f(x) = 2x

f(x) = 9x +4

**Explain Function and its Types** in Math

**There are various types of functions. Some are given below:**

Into function |

Onto Function ( Surjective Function ) |

(1_1) and Into Function (Injective Function ) |

(1_1) and Onto Function ( Bijective Function ) |

Linear Function |

Quadratic Function |

## Difference Between Into and Onto Function

**What does Into mean ****Function in Math**?

**Function in Math**?

If a function **f: A➝B** is such that Ran** f⊂B i.e**., Ran **f≠B**, then f is said to be a function from **A** into **B**.

In simple words:

A function is said to be into a function if every element of **A** is busy with elements of **B**.

**What does Onto mean in Math**

if a **function** f: A➝B is such that Ran f=B i.e., every element of B is the image of some elements of A, then f is called an onto function. It is also called the surjective function.

in simple words:

A function is said to be onto function if every element of B is also busy with elements of A.

**What is (1_1) and INTO (Injective) Function?**

if a function f from A into B is such that the second element of no two of its ordered pair are equal, then it is called an injective (1_1) and into function.

in simple words:

A function is said to be (1_1) and into an (injective) function if in B there is at least one nonbusy element.

** What is (1 _ 1) and ONTO Function (bijective function)?**

If f is a function from A onto B such that the second element of no two of its ordered pairs are the same, then f is said to be (1 *1) function from A onto B. Such functions are also called (1* 1) correspondence between A and B. It is also called bijective function.

In simple words: A function is said to be (1 _ 1) and onto function (bijective function) if every element of A is busy with every element of B.

**What does Linear Function Definition in Math?**

The function {(x,y) | y= mx + c} is called a linear function. Because its graph is a straight line.

**Define Quadratic Function** in Math?

**y = mx + c** or **ax + by + c= 0 **represents a straight line. This can be easily verified by drawing graphs of a few linear equations with numerical coefficients. The function **{ (x , y) | ax²** **+ bx + c}** is called a quadratic function because it is defined by a quadratic (second degree) equation in x , y.