Question

Select Is a Function or Is not a Function to correctly classify each relation. Title Is a Function Is not a Function

Answer 1

A mapping is said to be function if each element in the domain is related with only one element in the range.Or you can say that a relation is a function also when two different elements in domain have same image or related with same element of the Co domain.

The elements which is related with elements of domain is called Co domain.

So , using the definition of function that i have written above you can classify that the relation is a function or not

1. {(2, 2),(4, 4),(6, 6),(8, 8)}

→→Each element is related with itself , no two different images have different Preimage, For example (2,3),(2,4) that is not happening in this case. so this relation is a function.This kind of function is called identity function.

2. (0, 3),(3, 5),(5, 6),(8, 4)→Different element have different images .So this Relation is a function.

3. (1, 2),(3, 3),(4, 8),(6, 3) →→→Here two elements have same image 3. But still this is a function because two elements in domain or preimage can have same image in a function.

4. (3, 4),(5, 2),(5, 6),(7, 3)→→→This is not a function because two different elements of image have same preimage that is image of 2,and 6 have same preimage which is 5. So this is not a function.

From The given options 1,2,3 are functions.

Answer 2

{(2, 2),(4, 4),(6, 6),(8, 8)} Is a function.
{(0, 3),(3, 5),(5, 6),(8, 4)} Is a function.
{(1, 2),(3, 3),(4, 8),(6, 3)} Is a function.
{(3, 4),(5, 2),(5, 6),(7, 3)} Is not a function. 

For a relation to be a function, every x value must have only one y value.

Hope this helps.