Nothing really special about it. An ordered pair, commonly known as a point, has two components which are the x and y coordinates. As long as the numbers come in pairs, then that becomes a relation. If you can write a bunch of points ordered pairs then you already know how a relation looks like. For instance, here we have a relation that has five ordered pairs. Writing this in set notation using curly braces. However, aside from set notation, there are other ways to write this same relation.

We can show it in a table, plot it on the xy-axis, and express it using a mapping diagram. When listing the elements of both domain and range, get rid of duplicates and write them in increasing order. Just like a relation, a function is also a set of ordered pairs; however, every x-value must be associated to only one y-value.

Since we have repetitions or duplicates of x-values with different y-values, then this relation ceases to be a function. This relation is definitely a function because every x-value is unique and is associated with only one value of y.

So for a quick summary, if you see any duplicates or repetitions in the x-values, the relation is not a function. How about this example though? Is this not a function because we have repeating entries in x? Be very careful here. Yes, we have repeating values of x but they are being associated with the same value of y. The point 1,5 shows up twice, and while the point 3,-8 is written three times. This table can be cleaned up by writing a single copy of the repeating ordered pairs.

Each element of the domain is being traced to one and only element in the range. However, it is okay for two or more values in the domain to share a common value in the range. That is, even though the elements 5 and 10 in the domain share the same value of 2 in the range, this relation is still a function. What do you think? Does each value in the domain point to a single value in the range? This is a great example of a function as well.

Not really. The element 15 has two arrows pointing to both 7 and 9. This is a clear violation of the requirement to be a function.

### Relations and Functions

A function is well behaved, that is, each element in the domain must point to one element in the range. Therefore, this relation is not a function. A single element in the domain is being paired with four elements in the range. Remember, if an element in the domain is being associated with more than one element in the range, the relation is automatically disqualified to be a function.

Thus, this relation is absolutely not a function.If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Math 8th grade Linear equations and functions Recognizing functions.

Testing if a relationship is a function. Relations and functions. Recognizing functions from graph. Checking if a table represents a function. Practice: Recognize functions from tables. Recognizing functions from table.

Checking if an equation represents a function. Does a vertical line represent a function? Practice: Recognize functions from graphs. Recognizing functions from verbal description. Recognizing functions from verbal description word problem.

Next lesson. Current timeTotal duration Math: 8. Google Classroom Facebook Twitter. Video transcript Is the relation given by the set of ordered pairs shown below a function? So before we even attempt to do this problem, right here, let's just remind ourselves what a relation is and what type of relations can be functions. So in a relation, you have a set of numbers that you can kind of view as the input into the relation.

We call that the domain. You can view them as the set of numbers over which that relation is defined. And then you have a set of numbers that you can view as the output of the relation, or what the numbers that can be associated with anything in domain, and we call that the range. And it's a fairly straightforward idea. So for example, let's say that the number 1 is in the domain, and that we associate the number 1 with the number 2 in the range.

So in this type of notation, you would say that the relation has 1 comma 2 in its set of ordered pairs. These are two ways of saying the same thing. Now the relation can also say, hey, maybe if I have 2, maybe that is associated with 2 as well. So 2 is also associated with the number 2.Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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Related Topics: More Lessons for Grade 9 Math Worksheets Videos, worksheets, solutions, and activities to help Algebra 1 students learn how to distinguish between relations and functions and how to to solve real life problems that deal with relations. What is a relation? A relation is any set of ordered pairs.

What is a function? A function is a relation in which each x-element has only one y-element associated with it. Given a set of ordered pairs, a relation is a function if there are no repeated x-value. A relation is a function if there are no vertical lines that intersect its graph at more than one point. This is called the vertical line test. Table of Values - One way to represent the relationship between the input and output variables in a relation or function is by means of a table of values.

Ordered Pairs - Relations and functions can also be represented as a set of points or ordered pairs. Example: Which of the following sets of ordered pairs represent functions? One and only one output exists for each input. More than one value exists for some or all input value s. In general, we say that the output depends on the input. Show Step-by-step Solutions.An ordered-pair number is a pair of numbers that go together. The numbers are written within a set of parentheses and separated by a comma.

For example, 4, 7 is an ordered-pair number; the order is designated by the first element 4 and the second element 7. The pair 7, 4 is not the same as 4, 7 because of the different ordering. Sets of ordered-pair numbers can represent relations or functions. The following diagram shows some examples of relations and functions. Scroll down the page for more examples and solutions on how to determine if a relation is a function.

The pairing of the student number and his corresponding weight is a relation and can be written as a set of ordered-pair numbers. The set of all first elements is called the domain of the relation.

The set of second elements is called the range of the relation. The second element does not need to be unique. A function can be identified from a graph. If any vertical line drawn through the graph cuts the graph at more than one point, then the relation is not a function.

This is called the vertical line test. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page.

Please submit your feedback or enquiries via our Feedback page. In these lessons, we will look at ordered-pair numbers, relations and an introduction to functions. Relation A relation is any set of ordered-pair numbers.

Suppose the weights of four students are shown in the following table. Student 1 2 3 4 Weight The pairing of the student number and his corresponding weight is a relation and can be written as a set of ordered-pair numbers.Students often feel troubled because they cannot find the appropriate solutions for NCERT solutions for class 12 maths chapter 1 relations and functions.

Here, the learners will find the proper solutions to the sums of relation and function class 12 chapter. Students will have a recap of their learning from the previous class. The assessment will pave the way to a more in-depth understanding of the fundamental concepts of class 12 Maths Chapter 1.

A student will also learn the quantifiable relationship between two objects belonging to the sets.

### Chapter 1 Class 12 Relation and Functions

All the key points pertaining to relations and functions can be clearly understood with the given set of instructions. For a good understanding of the NCERT solutions for class 12 Maths Chapter 1, there is a need to revise the topics covered in the previous class.

Students will gain a refined understanding of the topics covered in Chapter 1 by studying the given activities. By going through the activities carefully, and by solving the sums of Chapter 1 they will be able to establish a clear idea of the properties of Relations and Functions.

## NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

The level of difficulty will be propelled from an easier stage to a difficult one as one goes on solving the sums, one after the other. After gaining an overall idea of Chapter 1, it will be easier for students to answer every question with the utmost clarity. A reiteration of these topics will help them to gain a deeper understanding of vertible and invertible functions. Comprehensive knowledge of real numbers and the usage of addition, multiplication, division, and subtraction will help them develop a better understanding of this chapter.

Along with this, an insight into how the usage of relations accentuates the complimentary integer is also included in this chapter. Furthermore, it will pave the way for understanding the domain and the co-domain that adheres to the principles of functions.

The above section explains the various types of Functions like identity function, constant function, polynomial function, rational function, modulus function, signum function, etc. This will help in understanding the relationship between the injective and the surjective function. One will also learn how the elements of three distinctly different numbers are in association with a host element. It furthermore provides a deeper sense of understanding about the finite as well as the infinite sets.

This section will focus on the composition of the functions and how the inverse quality concerning bijective works. Once you gain an understanding of this, you will be provided with examples exploring the relationship between the set and the codes.

This section of the chapter focuses on the combination of two distinctly different functions and how a code can be eventually attached to it. It will show how operational functions assist in inducing two numbers and therefore, their association as binary operations is used in the merging of two integers into one.Let A and B be two sets.

Types of Relations. Let f be a function from A to B. If every element of the set B is the image of at least one element of the set A i.

Otherwise we say that the function maps the set A into the set B. Functions for which each element of the set A is mapped to a different element of the set B are said to be one-to-one. A function can map more than one element of the set A to the same element of the set B. Such a type of function is said to be many-to-one. A function which is both one-to-one and onto is said to be a bijective function.

The order of the elements is taken into consideration, i. Class 12 Maths Chapter 1 Solutions in English. Class 12 Maths Chapter 1 Solutions in Hindi. Important Terms related to Chapter 1 Before studying this lesson, you should know: Concept of set, types of sets, operations on sets Concept of ordered pair and cartesian product of set.

Domain, co-domain and range of a relation and a function. Relation Let A and B be two sets. Equivalence Relation A relation R on a set A is said to be an equivalence relation on A iff it is reflexive it is symmetric it is transitive. Hence, R is neither reflexive, nor symmetric, nor transitive.

Hence, R is symmetric but neither reflexive nor transitive. Set A is the set of all books in the library of a college.

Hence, R is an equivalence relation. Therefore, R is an equivalence relation. Hence, this set of points forms a circle with the centre as the origin and this circle passes through point P. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

Also, P2 and P3 have the same number of sides. The elements in A related to the right-angled triangle T with sides 3, 4, and 5 are those polygons which have 3 sides Since T is a polygon with 3 sides. Hence, the set of all elements in A related to triangle T is the set of all triangles. Show that R is an equivalence relation.By Login, you agree to our Terms and Privacy Policies. Forgot Password?

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## NCERT Solutions for Class 12 Maths Chapter 1

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**NCERT - Class XII - RELATIONS AND FUNCTIONS - Solved Examples - Question No. 41**

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