functions assignment grade 11

MCR3U: FUNCTIONS GRADE 11 , UNIVERSITY PREPARATION SAMPLE EXERCISES ☰ Menu: Click to navigate this page

Discrete functions.

• Arithmetic and geometric sequences I
• Arithmetic and geometric sequences II
• Arithmetic and geometric series
• Compound interest and annuity

Exercises on characteristics of functions

• ASSIGNMENT on characteristics of functions
• Another ASSIGNMENT on characteristics of functions
• QUIZ on characteristics of functions
• Sample TEST on characteristics of functions
• Class exercise (#6) on functions and function notation
• Class exercise (#7) on domain and range
• Class exercise (#8) on inverse of a function
• Class exercise (#9) on multiplication and division of rational expressions
• Class exercise (#10) on addition and subtraction of rational expressions

Exercises on quadratics and transformations

• ASSIGNMENT on quadratics and transformations
• Another ASSIGNMENT on transformations
• Another ASSIGNMENT on rational expressions and transformations
• QUIZ on quadratics and transformations
• Sample TEST on quadratics and transformations
• Class exercise (#11) on completing the square
• Class exercise (#12) on combined transformations
• Class exercise (#13) on zeros of quadratics
• Class exercise (#14) on linear-quadratic systems

Exercises on exponential functions

• ASSIGNMENT on exponential functions
• QUIZ on exponential functions
• Sample TEST on exponential functions
• Class exercise (#15) on integral and rational exponents
• Class exercise (#16) on exponential growth and decay
• Class exercise (#17) on graphing exponential functions
• Class exercise (#18) on transformations of exponential functions

Exercises on trigonometric functions

• ASSIGNMENT on trigonometric functions
• Sample TEST on trigonometric functions
• Class exercise (#19) on trigonometric ratios
• Class exercise (#20) on trigonometry of obtuse angles
• Class exercise (#21) on applications of trigonometry
• Class exercise (#22) on understanding angles
• Class exercise (#23) on trigonometric identities and special angles
• Class exercise (#24) on periodic functions
• Class exercise (#25) on transformations of sinusoidal functions
• Sample final exam
• Sample culminating assignment

Exercises on discrete functions

• ASSIGNMENT on discrete functions
• QUIZ on discrete functions
• Sample TEST on discrete functions
• Class exercise (#1) on arithmetic and geometric sequences
• Class exercise (#2) on arithmetic and geometric series
• Class exercise (#3) on recursion
• Class exercise (#4) on binomial expansions using Pascal's triangle
• Class exercise (#5) on compound interest and annuity

Maybe you've experienced this as a teacher (irrespective of your teaching subject). You designed a home work or an assignment. You printed copies and distributed to your students. You gave them a day to submit the work. The day arrived. Then a particular student -- or some students -- didn't do the work. You asked why? In response, the student mentioned that (inadvertently) the work was misplaced (or lost). The student then asked for another copy of the exercise. You, the teacher, obliged and gave another copy of the exercise to the student. The incidence then repeats itself. This is one of the excuses some students give for not doing the exercises assigned to them. From our personal perspective, not many classroom experiences frustrate as much as the above. In a bid to obviate this, we came up with this website -- our initial objective was to make all exercises available to our students outside the classroom (and school) environment. Our approach may have been a drastic one, but it was also made possible by our interest in web development. We then have to print our exercises ONCE and only ONCE. If the student misplaces (or loses) the copy of the exercise, it is then the student's responsibility to print new copies from our website. It will follow that most of the exercises below reflect our teaching taste, and so may not appeal to a wide audience. In fact, they are patterned after the Ontario curriculum, and so their possible usefulness may be limited to this Canadian province. Also, we haven't provided solutions to them -- but we're working on this, including changing the format. In the meantime if you find any of these exercises useful, we'll be more than excited.

Free Printable functions Worksheets for 11th Grade

Math functions worksheets for Grade 11 students: Discover a variety of free printable resources to enhance your teaching and help students master essential mathematical concepts. Created by Quizizz.

10th - 11th

11th - 12th

Explore functions Worksheets by Grades

• kindergarten

Explore Other Subject Worksheets for grade 11

• social studies

Explore printable functions worksheets for 11th Grade

Functions worksheets for Grade 11 are essential tools for teachers who want to help their students master the fundamental concepts of Math, particularly algebra. These worksheets provide a variety of problems that focus on key topics such as linear and quadratic functions, domain and range, and function notation. Teachers can use these worksheets to supplement their lesson plans, provide additional practice for students who may be struggling with specific concepts, or even as a form of assessment to gauge students' understanding of the material. By incorporating functions worksheets for Grade 11 into their curriculum, educators can ensure that their students are well-prepared for more advanced mathematical studies.

Quizizz is an excellent platform for teachers who want to enhance their students' learning experience with functions worksheets for Grade 11, as well as other Math and algebra resources. This interactive platform allows educators to create engaging quizzes and games that can be used alongside traditional worksheets to reinforce key concepts and promote active learning. Teachers can also access a vast library of pre-made quizzes and worksheets, covering a wide range of topics and grade levels, making it easy to find the perfect resources for their specific needs. Additionally, Quizizz offers real-time feedback and analytics, allowing teachers to track their students' progress and identify areas where additional support may be needed. By utilizing Quizizz in conjunction with functions worksheets for Grade 11, educators can create a dynamic and effective learning environment that fosters a deep understanding of Math and algebra concepts.

Welcome to Grade 11 Functions! Use this page to find all resources worked on in class. Find course outlines, unit outlines, handouts, lessons and homework.

– Textbook –  Textbook answers  (back of the book) – Solution Manual, Chapters:  one   two   three   four   five   six   seven –  Link to blank notes – Link to lesson videos

Units of Study:

• Unit 1 – Functions [ Outline ]
• Unit 2 –  Transformations of Functions [ Outline ]
• Unit 3 – Exponential Functions [ Outline ]
• Unit 4 –  Trigonometry [ Outline ]
• Unit 5 –  Trigonometric Functions [ Outline ]
• Unit 6 –  Sequences and Series [ Outline ]
• Unit 7 –  Financial Applications [ Outline ]
• Review Stations [ Solutions ]
• Exam Review Questions w/ answers
• Old Exam w/ answers

• State Test Prep Blended program
• State Test Prep Online Program
• Summer Learning
• Writing Program
• Oral Reading Fluency Program
• Reading Skills Improvement Program
• After School Program
• High School Program
• Professional Development Platform
• Teacher PD Online Course
• Smart Communication Platform
• State Assessment Prep
• Classroom Tools
• State Test Teacher PD Course
• State Test Prep Blended Program
• Oral Reading Fluency Online Program
• Oral Reading Fluency Workbooks
• College Readiness – SAT/ACT
• High School Math & ELA
• Curious Reader Series
• For Libraries
• High School Math, Reading and Writing
• Online Professional Certification Exams
• Job Interview Practice Tool
• HR Software
• Online Pre-employment Assessment Platform
• Online Employee Training & Development Platform
• Enterprise Video Library
• Association Software
• Association Learning Management System
• Online Course Platform
• After-event Success Platform
• Self-service FAQ and Help Center
• Free Resources
• Success Stories
• Program Evaluation Reports

Grade 11 Math Questions and Solutions

The Smarter Balanced Assessment Consortium (SBAC) is a standardized test that includes various new technology-enhanced questions.

Some of them are Multiple choice-single correct responses, Multiple choice-multiple correct responses, Matching Tables, Drag and Drop, Hot text, Table Fill in, Graphing, Equation/numeric, Extended constructed response, Short answer, and many more.

This page contains several sample questions and practice test links for Grade 11 Math that give you an idea of questions that your students are likely to see on the test. After each sample question, an answer explanation follows. The explanation includes essential aspects of the task that you may need to consider for the skills, processes, and information your students need to know.

Domain: Grade 11 >> Number and quantity – The Real Number System

Sample Question: Multiply 36/49 and 21/63. What type of number is the result

• The numbers cannot be multiplied
• 57/112,rational
• 12/49,rational
• 12/49,irrational

Answer Explanation: Recall that a rational number is any number that can be expressed as a ratio or quotient of two integers (fractions). Irrational numbers are numbers that cannot be expressed as a fraction. Both numbers are fractions. Therefore, they are both rational numbers. Multiply them together and simplify the answer: 36/49.21/63=(4/7.9/7).3/9.7/7=12/49. The answer is a fraction. Thus, it is a rational number.

Standards: HSN.RN.B.3

Click here to practice: Number and quantity – The Real Number System Questions on Grade 11 Math

Domain: Grade 11 >> Number and Quantity – Quantities

Sample Question: The graph below shows the vibrations one of the strings on a violin when it is being played. What is true about the scale of the y-axis of the graph?

• Each mark on the y-axis could probably be one foot.
• Each mark on the y-axis could probably be one centimeter.
• Each mark on the y-axis could probably be one millimeter.
• Each mark on the y-axis could probably be one inch.

Answer Explanation: The graph represents the amplitude of the vibrating violin string. When the violin string follows this graph, the string is stretched in one direction and then in the other direction. Each time the string crosses the x-axis, it is in its original position. This motion is so small it is almost not seen by the human eye. Therefore the unit has to be very small. The smallest choice is millimeter.

Standards: HSN.RN.A.1

Click here to practice: Grade 11 Number and Quantity – Quantities Questions

Domain: Grade 11 >> Number and Quantity – The Complex Number System

Sample Question: What is the conjugate of the complex number 7+3i ?

Click here to practice: Grade 11 Math Number and Quantity – The Complex Number System Questions

Domain: Grade 11 >> Number and Quantity – Vector & Matrix Quantities

Sample Question: Subtract these two vectors ⟨−12,−23⟩−⟨−8,−14⟩.

Answer Explanation: The question asks us to subtract these two vectors ⟨−12,−23⟩−⟨−8,−14⟩ . If we have two vectors, v→=(x 1 ,y 1 )and w→=(x 2 ,y 2 ), then the difference of the two vectors is v→−w→=⟨x 1 −x 2 ,y 1 −y 2 ⟩ . In this question, we are subtracting ⟨−12,−23⟩−⟨−8,−14⟩ . The difference is ⟨−12−(−8),−23−(−14)⟩=⟨−4,−9⟩

Standards: HSN.VM.B.4

Click here to practice: Number and Quantity – Vector & Matrix Quantities Questions for Grade 11 Math

Domain: Grade 11 >> Algebra – Arithmetic with Polynomials & Rational Expressions

Sample Question: Subtract (x 3 +2x 2 -x+7) from (4x 3 +6x 2 +2x-7)

• -3x 3 +4x 2 +3x-14
• -3x 3 -4x 2 -3x+14
• 3x 3 +4x 2 +3x
• 3x 3 +4x 2 +3x-14

Answer Explanation: When combining polynomials, combine like terms by combining the coefficients. Subtract (x 3 +2x 2 -x+7) from (4x 3 +6x 2 +2x-7) (4x 3 }+6x 2 +2x-7) – (x 3 +2x 2 -x+7) (4x 3 -x 3 ) +(6x 2 -2x 2 ) +(2x-(-x)) +(-7-7) 3x 3 +4x 2 +3x-14

Standards: HSA.APR.A.1

Click here to practice: Algebra – Arithmetic with Polynomials & Rational Expressions Questions for Grade 11 Math

Domain: Grade 11 >> Algebra – Seeing Structure in Expressions

Sample Question: What is the coefficient of the third term the expression 5x 3 y 4 +7x 2 y 3 −6xy 2 −8xy?

Answer Explanation: The expression 5x 3 y 4 +7x 2 y 3 −6xy 2 −8xy is a polynomial expression with four terms. The coefficient of a term is the number in the front of the term. If the term begins with a negative, then the coefficient is a negative number, whether or not the term has variables. The third term is −6xy 2 and the number in the front of the term is -6.

Standards: HSA.SSE.A.1

Click here to practice: Algebra – Seeing Structure in Expressions Questions for Grade 11 Math

Domain: Grade 11 >> Algebra – Creating Equations

Sample Question: Madison is a sales associate for a transportation options dealer. Each month she sells two cars for every 10 bicycles and four motorcycles for every car. If she makes 40 sales per month, and the variable x represents the number of cars she sells, which equation could you use to find how many cars she sells?

• 2x+10x+8x=40
• 2x+10x+8x=20

Answer Explanation: If we use the variable x for the number of cars Madison sells, and she sells two cars for every 10 bicycles, then she sells five times as many bicycles as cars. Thus she sells 5x bicycles. Then, if she sells four motorcycles for every car, the number of motorcycles she sells is 4x. The problem states that she makes 40 sales per month, so add the cars, bicycles, and motorcycles up and make that sum equal to 40. The equation is x+5x+4x=40.

Standards: HSA.CED.A.1

Click here to practice: Algebra – Creating Equations Questions for Grade 11 Math

Domain: Grade 11 >> Algebra – Reasoning with Equations & Inequalities

Sample Question: What is the solution to 6x+5=101?

Answer Explanation: The question asks you to find the solution to 6x+5=101. Begin by subtracting 5 from both sides of the equation. This gives you 6x=96. Next, divide both sides by 6 and x=16.

Standards: HSA.CED.A.4

Click here to practice: Algebra – Reasoning with Equations & Inequalities Questions for Grade 11 Math

Domain: Grade 11 >> Functions – Interpreting Functions

Sample Question: The function f(x)=−1/8(x−7/2)2+3/2 is the path of a football at a practice game. Its graph is shown below. What portion of the domain of this function actually models this situation?

Answer Explanation: The function is a polynomial function. The domain of all polynomial functions, in a mathematical context, is (−∞,∞). However, in a real world context, the domain must allow the function to obey the rules of the real world. The ball is hit at time equals 0 seconds, and the ball lands, according to the graph, at time equals 7 seconds. Therefore, the domain is [0,7].

Standards: HSF.IF.B.5

Click here to practice: Functions – Interpreting Functions Questions for Grade 11 Math

Domain: Grade 11 >> Functions – Building Functions

Sample Question: How is the graph of f(x) = x + 7 different from g(x) = x + 12?

• When f(x) is shifted up 5 units, g(x) will be obtained
• g(x) is obtained by shifting f(x) down 5 units
• When g(x) is shifted up 5 units, f(x) will be obtained
• f(x) is obtained by shifting g(x) up 5 units

Answer Explanation: The value added to the function causes a vertical shift in the graph. Since 12 is 5 units larger than 7, the graph of g(x) is obtained by shifting f(x) 5 units up.

Standards: HSF.BF.B.3

Click here to practice: Functions – Building Functions Questions for Grade 11 Math

Domain: Grade 11 >> Functions – Linear, Quadratic, & Exponential Models

Sample Question: Which function is graphed below?

• f(x)=5(0.5) x
• f(x)=5(0.4) x
• f(x)=4(0.5) x
• f(x)=5(1.5) x

Answer Explanation: The graph shows that the function is an exponential growth function. The formula for an exponential function is f(x)=ab x , where a is the y-intercept and b is the growth factor. If the exponential function is a growth function, then b>1. If the exponential function is a decay function, then 0 x .

Standards: HSF.LE.A.2

Click here to practice: Functions – Linear, Quadratic, & Exponential Models Questions for Grade 11 Math

Domain: Grade 11 >> Functions – Trigonometric Functions

Sample Question: If cosσ=−1, what is the value of sinσ ?

Answer Explanation: Rule :

Standards: HSF.TF.C.8

Click here to practice: Functions – Trigonometric Functions Questions for Grade 11 Math

Domain: Grade 11 >> Geometry – Congruence

Sample Question: Suppose PQRS is translated as shown in the figure below. How is the parallelogram translated?

Answer Explanation: The figure shows that the translation is to the right and downward. Based on the figure, the distance the parallelogram is translated toward the right is the same as the length of side PQ. Additionally, based on the figure, the distance the parallelogram is translated downward appears to be approximately one-half of the length of side QR.

Standards: HSG.CO.A.4

Click here to practice: Geometry – Congruence Questions for Grade 11 Math

Domain: Grade 11 >> Geometry – Similarity, Right Triangles, & Trigonometry

Sample Question: Perform a dilation on point C centered at the origin with scale factor equal to 1/2. What is the coordinate of the resulting image point C’?

Answer Explanation: When dilation is performed about the origin, the coordinates of the image point are the product of the scale factor and the coordinates of the original point. ½*4 = 2. ½* -3 = -3/2.

Standards: HSG.SRT.A.1

Click here to practice: Geometry – Similarity, Right Triangles, & Trigonometry Questions for Grade 11 Math

Domain: Grade 11 >> Geometry – Circles

Sample Question: A tangent line is drawn to a circle from a point outside a circle. A radius is drawn from the center of the circle to the point of tangency of the line. What angle does the radius make with the tangent line?

Answer Explanation: A radius of a circle drawn to the point of tangency of a tangent line is perpendicular to the tangent line.

Standards: HSG.C.A.2

Click here to practice: Geometry – Circles Questions for Grade 11 Math

Domain: Grade 11 >> Geometry – Expressing Geometric Properties with Equations

Sample Question: When writing the equation y=x 2 +6x+7, Angelica used the following steps. If she made any mistakes, explain them and write the correct equation. y=x 2 +6x+7 y−7=x 2 +6x y−7−9=x 2 +6x+9 y−16=(x+3) 2 y=(x+3) 2 +16

Answer Explanation: To put the equation in standard form, we have to complete the square to get the squared binomial that is necessary for standard form. To complete the square, we take half of the coefficient of the linear term which will be 3, then square it and add it to both sides. Then factor the perfect square trinomial to get the squared binomial. Then solve for y.

Standards: HSG.GPE.A.2

Click here to practice: Geometry – Expressing Geometric Properties with Equations Questions for Grade 11 Math

Domain: Grade 11 >> Geometry – Modeling with Geometry

Sample Question: What is the density of a brick that occupies 310cm 3 with a mass of 853 g?

Answer Explanation: V = Bh = lwh Volume of a Rectangular Prism

The formula for density is d = m/V. The volume is given to be 310cm 3 and the mass is 853 g. Plug those values into the formula to find density.

Standards: HSG.MG.A.2

Click here to practice: Geometry – Modeling with Geometry Questions for Grade 11 Math

Domain: Grade 11 >> Geometry – Geometric Measurement & Dimension

Sample Question: A hemisphere with radius 3 cm sits atop a cone of equal diameter and height of 10 cm, as shown in the diagram below. Find the combined volume of the composite object.

Answer Explanation: The total volume of the object is the sum of the volumes of the hemisphere and the cone. V = ½ (4/3) πr 3 +(1/3)πr 2 h V = ½ (4/3) π(3m) 3 +(1/3)π(3m) 2 (10cm)V=48πcm 3

Standards: HSG.GMD.A.3

Click here to practice: Geometry – Geometric Measurement & Dimension Questions for Grade 11 Math

Domain: Grade 11 >> Statistics & Probability – Interpreting Categorical & Quantitative Data

Sample Question: What effect does a group of very large values have on the mean and median of a data set?

• The mean and the median are both increased
• The mean is not changed, but the median is increased
• The mean and median are not changed
• The mean is increased, but the median is decreased

Answer Explanation: The figure below shows the effect on the mean and median as a result of adding some very large elements to a data set. Since the new elements are very large, they have a significant effect on the mean because their very large values are averaged with the other values in the set. The median is also affected, and moves in the same direction as the mean moves.

Standards: HSS.ID.A.3

Click here to practice: Statistics & Probability – Interpreting Categorical & Quantitative Data Questions for Grade 11 Math

Domain: Grade 11 >> Statistics & Probability – Making Inferences & Justifying Conclusions

Sample Question: There are ten playing cards, four of them are red and six of them are black. Julian picks a card at random. What is the probability that he picks a red card?

Answer Explanation: Probability is calculated using the ratio of the number of successes divided by the number of possible choices.

The question asks for the probability of selecting a red card. There are four red cards out of a total of ten cards.

Thus, the probability of selecting a red card is four out of ten, which reduces to two out of five. That ratio is 2/5

Standards: HSS.IC.A.1

Click here to practice: Statistics & Probability – Making Inferences & Justifying Conclusions Questions for Grade 11 Math

Domain: Grade 11 >> Statistics and Probability – Conditional Probability & the Rules of Probability

Sample Question: The Venn diagram below shows the results of a survey on which sport people like to watch on television. Survey participants could choose one sport, two sports or all three sports. Which region(s) contains(s) responses in which a survey participant indicated that he/she like to watch only one sport?

Answer Explanation: Each circle contains the responses that like that specific color. Therefore, Regions A, B, C, E contain the responses that like to watch Baseball. Regions D, A, D, G contain the responses that like to watch Basketball. Regions A, B, D, F contain the responses that like to watch Football. If a letter is in two circles, the region contains responses that liked to watch the sports represented by both circles. If the region is in all three circles, that region contains the responses that like to watch all three sports. If the region is in only one circle, that region contains responses that stated that they only like to watch the sport represented by that circle. The regions that are in only one circle are E, F, G.

Standards: HSS.CP.A.1

Click here to practice: Statistics and Probability – Conditional Probability & the Rules of Probability Questions for Grade 11 Math

Domain: Grade 11 >> Statistics and Probability – Using Probability to Make Decisions

Sample Question: The Census Bureau provided a report that stated that the median income level of Floridians is 47,463. Based on this information, if you took a survey of 100 random workers in Florida, what is the probability the respondents’ income is greater than 47,463?

Answer Explanation: Median is the middle number when all numbers in the set are arranged from the least value to the greatest value. The question states that the median income level in Florida is 47,463, so one-half of the workers in Florida make less than 47,463 and one-half of the workers in Florida make more than 47,463. This means that, based on the Census Bureau’s report, the probability that a randomly selected person’s income is greater than 47,463 is 50% .

Standards: HSS.MD.A.4

Click here to practice: Statistics and Probability – Using Probability to Make Decisions Questions for Grade 11 Math

Looking for online practice tests? Here is the link to practice more of SBAC Grade 11 Math questions.

Related Links

Back-to-school Worksheets

Related posts:

No related posts.

Jenny Watson

About the author, one thought on “ grade 11 math questions and solutions ”.

Pingback: Summer is Here! Keep Your Child’s Literacy Skills Sharp with Online Games | Lumos Learning

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Notify me of follow-up comments by email.

Notify me of new posts by email.

Maths and Science Lessons

South Africa Maths and Science Lessons Online

Grade 11 – Functions

• Improve marks and help you achieve 70% or more!
• Provide learner with additional knowledge and understanding of the topic
• Enable learner to gain confidence to study for and write tests and exams on the topic
• Provide additional materials for daily work and use on the topic
• Provide materials for learners to access on their phones, tablets or computers at home or anywhere!
• Support knowledge, grasp and understanding, by completing a digital, interactive assignment
• Earn a badge for having successfully completed the tutorial and assignment.

Format of tutorial:

• View introductory videos
• Study content slides on the topic (1 – 2 hours in total)
• Complete the interactive assignment (30 min in total).

Course Content

Introduction to functions, linear and quadratic functions, quadratic functions, hyperbolic and exponential functions, exponential functions, average gradient – pdf, average gradient – video, trig functions, functions caps, quiz – functions.

• 0 R 0.00

Original EdwardsMaths Papers

Grade 11 Model Assignments

• 18164 Download
• 2.95 MB File Size
• 5 File Count
• December 26, 2018 Create Date
• January 19, 2019 Last Updated

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Grade 12 Math Mock Exam Limpopo September 2023 P2

Grade 12 math mock exam limpopo september 2023 p1, grade 12 math mock exam kzn september 2023 p1, grade 12 math mock exam eastern cape september 2023 p2, grade 12 math mock exam eastern cape september 2023 p1.

© 2018 All rights Reserved.

• Math Article

Relations and Functions Class 11

In relations and functions Class 11, you will learn the cartesian product of sets along with relations and functions. In our day-to-day life, we have known the term relations in a pattern such as the relation between brothers and sisters, husband and wife or teacher and student. In Maths, the term relation is used to relate the numbers, symbols, variables, sets, group of sets, etc. For example, A is a subset of B denotes the relation of A and B. A function is a kind of relation which is operated between two quantities to yield output.

In this article, we will provide you with the relations and functions class 11 notes, so that it would be easier for you to learn and understand the concepts.

Relations and Functions Class 11 Chapter 2

Before we start learning about relations and functions class 11, let us go through some basics of sets. As we learned, a set is a collection of objects or elements. You have also learned about the empty set, universal set and all the other types in sets for class 11. Let us learn here, the cartesian product of sets, as this concept will be used further to explain relations and functions for class 11 solutions.

Cartesian Product of Sets

Suppose there are two non-empty sets A and B. So, the cartesian product of A and B is the set of all ordered pairs of elements from A and B.

A × B = {(a,b) : a ∊ A, b ∊ B}

Let A = {a 1 , a 2 , a 3 , a 4 } and B = {b 1 , b 2 }

Then, The cartesian product of A and B will be;

A × B = {(a 1 , b 1 ), (a 2 , b 1 ), (a 3 , b 1 ), (a 4 , b 1 ), (a 1 , b 2 ), (a 2 , b 2 ), (a 3 , b 2 ), (a 4 , b 2 )}

Example: Let us say, X = {a,b,c} and Y = { 1,2,3}

Therefore, X × Y = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3), (c, 1), (c, 2), (c, 3)}.

This set has 9 ordered pairs. We can also represent it as in a tabular form.

Note: Two ordered pair X and Y are equal, if and only if the corresponding first elements and second elements are equal.

Definition: A relation R is the subset of the cartesian product of X x Y, where X and Y are two non-empty elements. It is derived by stating the relationship between the first element and second element of the ordered pair of X × Y. The set of all primary elements of the ordered pairs is called a domain of R and the set of all second elements of the ordered pairs is called a range of R.

For two sets X = {a, b, c} and Y = {apple, ball, cat}, the cartesian product have 9 ordered pairs, which can be written as;

X × Y = {(a, apple), (a, ball), (a, cat), (b, apple), (b, ball), (b, cat), (c, apple), (c, ball), (c, cat)}

With this we can obtain a subset of X x Y by introducing a relation R, between the elements of X and Y as;

R = {(a,b) : a is the first letter of word b, a ∊ X, b ∊ Y}

Therefore, the relation between X and Y can be represented as;

R = {(a,apple),(b,ball),(c,cat)}

Example : Let X={a,b} and Y = {c,d}. Find the number of relations from X to Y.

Solution : X × Y = {(a,c),(a,d),(b,c),(b,d)}

Number of subsets, n (X × Y) = 2 4 . Therefore, the number of relations from X to Y is 2 4 .

A relation ‘f’ is said to be a function, if every element of a non-empty set X, has only one image or range to a non-empty set Y.

If ‘f’ is the function from X to Y and (x,y) ∊ f, then f(x) = y, where y is the image of x, under function f and x is the preimage of y, under ‘f’. It is denoted as;

Example: N be the set of Natural numbers and the relation R be defined as;

R = {(a,b) : b=a 2 , a,b ∈ N}. State whether R is a relation function or not.

Solution: From the relation R = {(a,b) : b=a 2 , a,b ∈ N}, we can see for every value of natural number, their is only one image. For example, if a=1 then b =1, if a=2 then b=4 and so on.

Therefore, R is a relation function here.

Recommended Videos

Relations and types of relations.

Functions – Introduction, Co-domain and Range

  Learn more Maths topics with us and download BYJU’S -The Learning App.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

Visit BYJU’S for all Maths related queries and study materials

Your result is as below

Request OTP on Voice Call

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Post My Comment

The relation of maths subject is not so much strong than the relation between byjus and ours. Byjus is so much famous learning app. It is mainly by the exprience teachers. Thank you dear teachers.

Happy teachers day

Please visit: https://byjus.com/maths/relations-and-functions/ To learn more

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.