IGCSE Domain and Range of Functions: Complete Guide for Cambridge IGCSE Mathematics

IGCSE domain and range of functions are essential function topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering finding domain and range, function notation, and function properties is essential for understanding functions completely.

This comprehensive IGCSE domain and range of functions guide covers everything you need to know, including what domain and range are, how to find them, function notation, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to find the domain and range of functions, understand function notation, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Domain and Range of Functions Matter

IGCSE domain and range of functions are essential function topics. Here’s why they’re so important:

• High frequency topic: Domain and range questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for understanding functions and their properties
• Exam weight: Typically worth 4-7 marks per paper
• Real-world applications: Used in modeling and function analysis
• Problem-solving skills: Develops understanding of function behavior

Key insight from examiners: Students often confuse domain and range or struggle with restrictions. This guide will help you master these systematically.

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Understanding Domain and Range

Domain: All possible input values (x-values) for a function Range: All possible output values (y-values) for a function

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Finding Domain

The domain is usually all real numbers unless there are restrictions.

Restrictions:

• Division by zero: Exclude values that make denominator zero
• Square roots: Exclude values that make expression negative

Example 1: Find the domain of f(x) = 1/(x - 3)

Solution: Denominator cannot be zero: x - 3 ≠ 0, so x ≠ 3 Domain: All real numbers except 3

Answer: x ∈ ℝ, x ≠ 3

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Finding Range

The range depends on the function type and domain.

Example 2: Find the range of f(x) = x² + 1

Solution: Since x² ≥ 0, we have x² + 1 ≥ 1 Range: All real numbers ≥ 1

Answer: y ≥ 1 or [1, ∞)

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Function Notation

f(x) means “function of x” or “f evaluated at x”

Example 3: If f(x) = 2x + 3, find f(5)

Solution: f(5) = 2(5) + 3 = 13

Answer: 13

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Common Examiner Traps

• Confusing domain and range - Domain = inputs (x), Range = outputs (y)
• Forgetting restrictions - Check for division by zero and negative square roots
• Notation errors - Use correct mathematical notation

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Practice Questions

Question 1

Find the domain of f(x) = √(x - 2)

Solution: Expression under square root must be ≥ 0: x - 2 ≥ 0, so x ≥ 2 Domain: x ≥ 2

Answer: x ≥ 2

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Frequently Asked Questions About IGCSE Domain and Range of Functions

What is the domain of a function?

The domain is all possible input values (x-values) for which the function is defined.

What is the range of a function?

The range is all possible output values (y-values) that the function can produce.

How do I find restrictions on the domain?

Look for division by zero (denominator = 0) or negative values under square roots.

What does f(x) mean?

f(x) means “function of x” - it represents the output when x is the input.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Graphs of Functions: Complete Guide - Master function graphs
• IGCSE Quadratic Functions: Complete Guide - Master quadratic functions
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Domain and Range of Functions with Tutopiya

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