## What makes a function one-to-one and onto?

A function f from A to B is called one-to-one (or 1-1) if whenever f (a) = f (b) then a = b. No element of B is the image of more than one element in A. In a one-to-one function, given any y there is only one x that can be paired with the given y. Such functions are referred to as injective.

Which relation is both one-to-one and onto?

A function f from A (the domain) to B (the range) is BOTH one-to-one and onto when no element of B is the image of more than one element in A, AND all elements in B are used. Functions that are both one-to-one and onto are referred to as bijective. Bijections are functions that are both injective and surjective.

### What is many-one and onto function?

The function f is a many-one (as the two elements have the same image in Y) and it is onto (as every element of Y is the image of some element X). So, it is many-one onto function.

How do you determine if a function is one-to-one onto both or neither?

If the graph of a function f is known, it is easy to determine if the function is 1 -to- 1 . Use the Horizontal Line Test. If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 .

## Can a function be onto but not one-to-one?

Let f(x)=y , such that y∈N . Here, y is a natural number for every ‘y’, there is a value of x which is a natural number. Hence, f is onto. So, the function f:N→N , given by f(1)=f(2)=1 is not one-one but onto.

Which graph is a one to one function?

Horizontal Line test: A graph passes the Horizontal line test if each horizontal line cuts the graph at most once. Using the graph to determine if f is one-to-one A function f is one-to-one if and only if the graph y = f(x) passes the Horizontal Line Test.

### Which does not represent a one to one function?

An easy way to determine whether a function is a one-to-one function is to use the horizontal line test on the graph of the function. To do this, draw horizontal lines through the graph. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function.

Is a Bijection one-to-one and onto?

With this terminology, a bijection is a function which is both a surjection and an injection, or using other words, a bijection is a function which is both “one-to-one” and “onto”.

## How do you determine if a function is one to one?

What is an example of a function that is not one to one?

For example, the quadratic function, f(x) = x2, is not a one to one function. Let’s look at its graph shown below to see how the horizontal line test applies to such functions. As you can see, each horizontal line drawn through the graph of f(x) = x2 passes through two ordered pairs.

### Which is one to one and which is onto?

is one-to-one (injective) if maps every element of to a unique element in . In other words no element of are mapped to by two or more elements of . . is onto (surjective)if every element of is mapped to by some element of . In other words, nothing is left out.

How are one to one and onto functions defined?

One-to-One/Onto Functions. Here are the definitions: is one-to-one (injective) if maps every element of to a unique element in . In other words no element of are mapped to by two or more elements of . . is onto (surjective)if every element of is mapped to by some element of . In other words, nothing is left out. .

## What is the definition of one to one?

Here are the definitions: is one-to-one (injective) if maps every element of to a unique element in . In other words no element of are mapped to by two or more elements of . . is onto (surjective)if every element of is mapped to by some element of .

How to determine if T is one to one or onto?

Observe that T[ 1 0 0 − 1] = [1 + − 1 0 + 0] = [0 0] There exists a nonzero vector →x in R4 such that T(→x) = →0. It follows that T is not one to one. The above examples demonstrate a method to determine if a linear transformation T is one to one or onto.