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Class 9 Mathematics Chapter 2 Relations and Functions Important Questions with Solutions
Relations and Functions is one of the most foundational chapters in Class 9 Mathematics, forming the backbone of higher algebra and calculus. This chapter teaches students how to understand relationships between sets, identify functions, and work with domain and range—skills essential for board exams and competitive tests. Our collection of important questions with detailed solutions helps you master every concept, from ordered pairs to function notation, using real NCERT-aligned examples and problem-solving strategies.
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What Are Relations and Functions? Understanding the Basics
A relation is any connection between elements of two sets, while a function is a special relation where each input has exactly one output. In NCERT Class 9, you'll learn that if A and B are sets, a relation from A to B is a subset of the Cartesian product A × B. Functions are denoted as f: A → B, where A is the domain and B is the codomain. Understanding this distinction is critical for solving questions about identifying whether a relation qualifies as a function.
Domain, Codomain, and Range: Key Definitions and Examples
The domain of a function is the set of all possible input values (x-values), the codomain is the set where outputs are supposed to belong, and the range is the set of all actual outputs. For example, if f(x) = 2x and the domain is {1, 2, 3}, the range is {2, 4, 6}. NCERT emphasizes that range is always a subset of codomain. Many board exam questions test whether students can correctly identify these three components from given relations.
Cartesian Product and Ordered Pairs Explained
The Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. If A = {1, 2} and B = {a, b}, then A × B = {(1,a), (1,b), (2,a), (2,b)}. The number of ordered pairs in A × B equals |A| × |B|. Understanding Cartesian products is essential because relations are defined as subsets of these products. NCERT Chapter 2 includes multiple worked examples to build clarity on this concept.
Types of Functions: One-to-One, Onto, and Bijective
Functions are classified based on how inputs map to outputs. A one-to-one (injective) function maps different inputs to different outputs. An onto (surjective) function covers every element in the codomain. A bijective function is both one-to-one and onto—these are invertible functions. Class 9 problems often ask students to determine function types using arrow diagrams or set notations, skills that prepare you for advanced mathematics.
Representation of Functions: Arrow Diagrams, Tables, and Graphs
Functions can be represented visually using arrow diagrams (showing connections between domain and range elements), as ordered pairs, in tabular form, or as graphs on a coordinate plane. NCERT Chapter 2 emphasizes that the vertical line test confirms whether a graph represents a function—if any vertical line intersects the graph more than once, it's not a function. Each representation method helps visualize relationships differently and is important for exam questions.
Real-Life Applications of Relations and Functions
Relations and functions appear everywhere: temperature as a function of time, cost as a function of quantity, or student marks as a function of study hours. These practical examples make abstract concepts tangible. NCERT includes real-world scenarios to help students understand why functions matter beyond textbooks. Board exams increasingly test conceptual application, so recognizing functions in daily life strengthens problem-solving ability.
Why CBSETUTOR.ai Is India's Most-Used AI Tutor for CBSE Mathematics
CBSETUTOR.ai is trusted by thousands of CBSE families across India to master chapters like Relations and Functions. Our AI-powered platform provides instant, personalized solutions to practice questions, step-by-step explanations aligned with NCERT, and adaptive learning paths that adjust to your pace. With 24x7 availability in both English and Hindi mediums, CBSETUTOR.ai ensures no student is left behind. Teachers and parents recommend us because we combine pedagogical rigor with technology to deliver results that show in board exams.
Important Questions on Relations and Functions with Solutions
CBSE board exams regularly test: (1) Identifying whether a relation is a function from a given set of ordered pairs; (2) Finding domain and range from equations like f(x) = 1/(x–2); (3) Determining if functions are one-to-one or onto using arrow diagrams; (4) Counting elements in Cartesian products; (5) Solving word problems involving functional relationships. Our question bank includes 2-mark, 3-mark, and 5-mark problems with complete solutions to help you prepare systematically.
Common Mistakes Students Make and How to Avoid Them
Students often confuse domain with range, forget that every input must map to exactly one output in a function, or incorrectly count ordered pairs in Cartesian products. Another frequent error: assuming codomain equals range. Practice with NCERT-aligned problems and use our AI tutor to get instant feedback when you slip up. Understanding why a mistake happens—not just the correct answer—builds deep conceptual mastery.
Preparation Strategy: How to Master This Chapter Before Your Exam
Start by clearly defining all key terms (relation, function, domain, codomain, range, injective, surjective, bijective). Work through NCERT textbook examples step-by-step, then attempt our curated important questions. Use arrow diagrams and graphs to visualize functions. Review past CBSE sample papers to understand question patterns. Take online tests to gauge readiness. With consistent practice over 2–3 weeks and guidance from CBSETUTOR.ai, you'll build confidence and accuracy.
Frequently asked questions
What is the difference between a relation and a function?+
A relation is any set of ordered pairs from two sets. A function is a special relation where each input (domain element) maps to exactly one output (range element). If one input maps to multiple outputs, it's a relation but not a function.
How do I find domain and range from an equation like f(x) = √(x – 3)?+
For f(x) = √(x – 3), the expression under the square root must be non-negative: x – 3 ≥ 0, so x ≥ 3. Domain = [3, ∞). Since the square root of a non-negative number is always non-negative, Range = [0, ∞).
Is CBSETUTOR.ai available for Hindi-medium students?+
Yes. CBSETUTOR.ai supports both English and Hindi mediums for all CBSE chapters including Relations and Functions. Our AI tutor explains concepts and solutions in your preferred language, making learning more comfortable and effective.
Can I use CBSETUTOR.ai for free before committing?+
Absolutely. CBSETUTOR.ai offers a free trial so you can experience our platform, explore practice questions, and see how personalized AI tutoring works. No credit card required to start learning today.
What is a bijective function?+
A bijective function is both injective (one-to-one) and surjective (onto). Every element in the domain maps to a unique element in the codomain, and every element in the codomain is mapped to by some domain element. Bijective functions are invertible.
How many ordered pairs are in the Cartesian product of two sets?+
If set A has m elements and set B has n elements, then A × B has m × n ordered pairs. For example, if A = {1, 2, 3} and B = {a, b}, then A × B contains 3 × 2 = 6 ordered pairs.
What does the vertical line test tell us about graphs?+
The vertical line test states that a graph represents a function if and only if every vertical line intersects the graph at most once. If any vertical line crosses the graph twice or more, the relation is not a function.
Where can I get step-by-step solutions to important questions on this chapter?+
CBSETUTOR.ai provides detailed, step-by-step solutions to all important Class 9 Mathematics questions aligned with NCERT. Our AI explains each step so you understand the 'why' behind the answer, not just the final result.
Related resources
NCERT Solutions for Class 9 Mathematics Chapter 2: PolynomialsNCERT Solutions for Class 9 Mathematics Chapter 1: Number Systems – Complete GuideClass 9 Mathematics Chapter 1: Number Systems — Complete Notes & Revision GuideClass 9 Mathematics Chapter 2: Polynomials – Complete Study Notes & Revision GuideNCERT Solutions for Class 9 Mathematics Chapter 3: Coordinate GeometryClass 9 Coordinate Geometry Chapter 3: Cartesian System & Plotting PointsNCERT Solutions for Class 9 Mathematics Chapter 4: Linear Equations in Two VariablesClass 9 Mathematics Chapter 1 Important Questions: Orienting Yourself — The Use of Coordinates
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