Relation and Function Examples

Example 1: Find the cartesian products of set A = {1, 2, 3} and B={3, 4, 5}. 

Solution:

Following the above definition, let Cartesian product be R, 

R = A ⨯ B 

   = {(1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,3), (3,4), (3,5)}

Example 2: Verify if ƒ(x) = x² is a function or not.

Solution: 

Here, the function takes a number as input. So its domain is all real numbers and in the output it gives the square of that number as output. So the co-domain will be all the positive numbers. 

Now, according to the definition of Function for each element of domain, it should give a unique output but vice versa is not true.

For example: here, x = -2 and 2 both give the same output 4. 

Since the condition is not violated, it will be considered as a function. 

Example 3: A relation is given in the table below, find out whether this relation is a function or not. 

Answer: 

In the above table the elements 1 and 3 in the image column i.e. have a common pre-image 2 which violates the definition of function that no two or more images can have a common pre image. Hence, the given relation is not a function.

Example 4: A relation is given in the table below, find out whether this relation is a function or not. 

Answer: 

In the above relation, each input has only one corresponding range value. So, this relation is a function.  

Example 5: Find out the range of function: ƒ(x) = 

Solution: 

Since the value inside the root cannot be negative, x² should be less than 16. 

That means x ∈ [-4,4]. This is domain of the function. 

For the range, let y= then y² = 16 – x²

or x²= 16 – y²

Since x ∈ [– 4, 4]

Thus range of f = [0, 4]

Example 6: Plot the graph of function f(x) = |x|. 

Solution:

The above function is a modulus function. In case of modulus function, f(x) = x if x > 0 and -x otherwise. The graph for the same is given below:

It can be noticed that in this, there are multiple inputs mapping to same value of the function. For Example: x = -2 and x = 2 both give f(x) = 2. 

Relation and Function are two ways of establishing links between two sets in mathematics. Relation and Function in maths are analogous to the relation that we see in our daily lives i.e., two persons are related by the relation of father-son, mother-daughter, brother-sister, and many more. On a similar pattern, two numbers can be related to each other as one number is the square of another number and many more. A function is a special kind of relation that is defined as a unique relation between two mathematical entities.

Relation and Functions are introduced in Class 11, and in Class 12 more advanced subtopics are taught in CBSE Syllabus. In this article, we will learn about relation and function, their definitions, relation and function examples, their representation, terms related to them, and the difference between relation and function in detail.