# What is the Difference Between Into and Onto Function

## 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.

f(x) = 2x

f(x) = 9x +4

### Explain Function and its Types in Math

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

## Difference Between Into and Onto Function

### What does Into mean 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.