Relations and Functions Worksheet

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Definition of Relation

A relation is established between two sets when an object from one set is related to one object from another set, resulting in the formation of ordered pairs. For instance, x is an object of set A and y is an object from set B. Then they share a relationship and can be written as an ordered pair (x, y).


Definition of Function

To define, a function is a binary process or relation that makes each element of one set somehow related to exactly one element from the second one.

Now, let’s begin with the relations functions worksheet.


Practise Worksheet Relations and Functions

1. P x P is a Cartesian product having nine elements. Already known sets of ordered pairs are (-2, 0) and (0, 2). Find set P and the remaining ordered pairs.

2. 120 students are studying in class 11 divided among four sections. Now consider set A to be the students and B to be the sections. Form a relation from A to B to show whether the students belong to any of the four sections. Also mention whether this relation is a function or not.

3. Expression to convert Fahrenheit to Celsius is y = (5x/9) – (160/9). Evaluate the inverse and also rule out whether the same is a function or not.

4. Find out whether the following statements are true or false.

(a) Relation {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} is a function also.

(b) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} is not a function.

(c) All functions are relations, but all relations are not functions.

(d) P = (1, 2, 3} and Q = {e, f}. P x Q provides number of relations to be 64.

(e) {(x,y) | x=3 and y is a real number} is both a function and relation.

5. R is a relation {(6,4), (8,-1), (x,7), (-3,-6)}. Find the value of x that will make this relation a function.

6. Consider n (A) = m and n (B) = n. Find out the number of relations (non-empty) that can be predicted from A to B.

7. f (x) = x3 – 1 / x3

What will be f(x) + f(1/x)?

8. Find the range and domain of a real function ‘f’ represented by f(x) = root over (x -1).

9. What will be the domain and range of the following relation?

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10. The following table contains data of a woman’s forehand with her respective height. With this data, a student maps a relationship between forehand and hand in the form y = ax + b, provided both are constants.


Height (y)

Length of forehand (x)

65.5

45.5

56

35

65

45

69.5

50

74

55


Determine whether this relation is a function or not, and find the values of both a and b.

11. If f (x) = 2x – 3, then find [f (0) + (f)] / 2 and value of x when (a) f(x) = 0 (b) f(x)= x and f(x) = f(1-x)

12. Consider an aeroplane moving at a velocity of 500 km per hour. Illustrate the travelled distance in the form of function t in hours.

13. Map the following relation and also mention the domain and range.

{(-2, 1), (0, 3), (5, 4), (-2, 3)}


Relations and Functions Worksheet Answer Key

1. Set P = {-2,0,2} and the remaining elements are {(-2,-2), (-2,2), (0,-2), (0,0), (2,-2), (2,0), (2,2)}

2. As all the 120 students belong to class 11, every pupil must be in any of the sections. So, this relation is a function as well.

3. f-1 (x) = (9x/5) + 32 and the inverse is a function also.

4. (a) True (b) False (c) True (d) True (e) False

5. 1

6. 2mn – 1

7. 0

8. Domain = (1, ∞) and Range = (0, ∞)

9. Range = {4, 16, 25, 36} and Domain = {-2, 2, 4, 5, 6}

10. As every value of x has a different value of y; it is a function. The value of a is 0.90 and b is 24.5

11. Value of [f(0) + f(1)] / 2 is -2, (a) x = 3/2 (b) x = 3 (c) x = ½

12. Required distance is 500t

13. Domain = {-2, 0, 5}, Range = {-1, 3, 4}


Mapping Figure:

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This relations functions worksheet may act as a last-minute tool to revise the function and relation problems before your exams. You must try to solve the questions on your own and later check it with the given practice worksheet relations and functions answer key.


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FAQ (Frequently Asked Questions)

1. How to Determine Whether a Given Relation is a Function or Not?

Ans. To determine whether a given relation is a function or not, one needs first to find out the input values, then the output values. After that, check whether each input value has a corresponding out value. If all these pointers match, then the relation is proved to be a function.

2. What are the Types of Functions in Mathematics?

Ans. In mathematics, a student will get to study multiple kinds of functions, which are one – one, many – one, onto, into, polynomial, linear, identical, quadratic, rational, cubic, algebraic, modulus, signum, greatest integer, fractional part, even and odd, periodic, composite, constant, identity, etc.

3. What is Meant by Well-defined and Undefined Function?

Ans. An expression is considered to be unambiguous or well-defined when the definition of the same allocates a unique value or interpretation. For the case of a function, a well-defined function will provide the same result if the input representation is altered, but the input value will not be changed. On the other hand, an undefined function is the one whose points are outside the domain. For instance, f(x) = root over x is an undefined function when the value of x is negative.