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.
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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FAQs on Relations and Functions Worksheet
1. What key concepts from relations and functions should students focus on for CBSE Class 11 exam preparation as per the latest worksheet trends?
Students should prioritise the understanding of types of relations, function definition, distinctions between one-one, onto, and many-one mappings, calculation of domain and range, and application of real-life scenarios such as temperature conversion or distance mapping. Mastery in identifying whether a relation is a function and solving exam-oriented problem types is essential for scoring well.
2. How are relations and functions differentiated in CBSE Class 11 board exams?
A relation describes a link between elements of two sets, while a function is a specific type of relation where every input has a unique output. In board exams, students must correctly justify if each mapping is a function by checking for repeated inputs with different outputs.
- All functions are relations.
- Not all relations are functions.
3. What types of exam questions are most commonly asked from the relations and functions worksheet section?
CBSE board exams commonly include questions on:
- Identifying and defining relations and functions from sets of ordered pairs.
- Finding the domain and range.
- Testing if a mapping or given statement is a function.
- Inverse of functions.
- Word problems involving real-life applications of relations and functions.
4. How do board exam markers assess the importance of domain and range in worksheet questions?
Markers award points for correctly identifying the domain (all possible valid inputs) and range (all possible outputs) for both relations and functions. Mistakes such as including values where the function is undefined (e.g., division by zero, square root of a negative) can lead to loss of marks. Accurate specification showcases a solid grasp of the topic as required in the syllabus.
5. What are the most frequent misconceptions students face with functions in CBSE worksheet questions?
Common misconceptions include:
- Assuming any assignment of values is a function, even when inputs have multiple outputs.
- Confusing the domain with the range.
- Overlooking restrictions such as undefined expressions.
- Misinterpreting the requirements for invertibility of functions.
6. How does the marking scheme weight questions from relations and functions in Class 11 Maths board exams?
Relations and functions typically carry multiple short and long answer questions ranging from 1 to 5 marks each.
- Direct definitions and true/false: 1 mark
- Example-based identification or calculation: 2–3 marks
- Detailed problem-solving, mapping, or inverse determination: 4–5 marks
7. What strategies should students use to identify or construct functions for 5-mark relation/function worksheet questions?
Students should:
- Clearly define sets and establish all possible ordered pairs.
- Check that each domain element maps to only one range element.
- Explicitly state domain, range, and mapping rule.
- Provide justification with examples and counterexamples where needed.
- Structure answers stepwise for clarity, as per CBSE marking guidelines.
8. Why are inverse functions and their properties considered important in exam-oriented relation and function worksheets?
Inverse functions are often tested because they validate whether a function is one-to-one and help students apply functional relationships in reverse scenarios. This plays a critical role in advanced mathematics and directly aligns with higher-order thinking skills required by the CBSE board.
9. How can one use example problems from worksheets to quickly revise relations and functions before the exams?
Reviewing solved examples from worksheets provides stepwise methods to solve varying question patterns seen in board exams. It reinforces identification of relations vs. functions, finding domains and ranges, and working with real-life mappings. Practising such problems helps in retaining concepts and improves accuracy in the actual exam.
10. In what ways do CBSE Class 11 worksheets improve understanding of HOTS (Higher Order Thinking Skills) questions on relations and functions?
Worksheets integrate application-based problems that make students apply concepts to unfamiliar situations, enhancing critical thinking. Questions such as constructing a function from real-world data or analyzing the impact of domain restrictions foster deeper reasoning, as required for HOTS in board exams. This improves preparedness for challenging and marks-heavy questions.
