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Function Notation, Domain and Range Revision Notes | IGCSE Edexcel Higher Maths

The domain is the set of input values a function is allowed to take. Use the allowed inputs to find the outputs they produce. Free IGCSE Maths notes.

Updated 25 Mar 2026 · Revise Right Team

Function Notation, Domain and Range is part of Functions, Coordinates and Linear Graphs in IGCSE Edexcel Higher Maths.

1 min

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IGCSE Edexcel Higher

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What this lesson covers

The domain is the set of input values a function is allowed to take. Use the allowed inputs to find the outputs they produce. Free IGCSE Maths notes.

Use function notation such as f(x) and g(3) accurately
Identify the domain of a function in a simple algebraic or real-world context
Describe the range produced by a rule or a graph

Key ideas to keep in view

Use this lesson to stay inside Functions, Coordinates and Linear Graphs while connecting the detail back to the wider Topic 3: Sequences, Functions and Graphs topic.

Function: A rule that gives one output for each permitted input.
Domain: The set of input values a function is allowed to take.
Range: The set of output values produced by the function.

Revision notes

Read the core explanations from Function Notation, Domain and Range before testing yourself from memory.

1. What This Lesson Covers

Function notation is not just shorthand. It helps you separate the rule from the value produced by a chosen input.

Domain and range matter because not every algebraic expression makes sense for every input, especially in real contexts or when a graph is restricted.

2. Key Vocabulary

4. Core Method

Read f(3) as the output when the input is 3, not as f multiplied by 3.
Use the question or the graph to decide which inputs are allowed. This gives the domain.
Then look at the outputs those inputs actually produce. This gives the range.
Check whether the context rules out negative values, impossible lengths, or excluded points.

6. Worked Examples

Worked example: Using notation and finding outputs

Given f(x) = 2x - 1, work out f(4) and f(-2).

f(4) = 2(4) - 1 = 7 — The output for input 4 is 7.
f(-2) = 2(-2) - 1 = -5 — Negative inputs are allowed here unless the question restricts them.

Answer: f(4) = 7 and f(-2) = -5

Worked example: Choosing a domain and range from context

A taxi fare is modelled by C = 4 + 1.5m where m is the journey distance in miles and 0 ≤ m ≤ 10.

0 ≤ m ≤ 10 — Distance cannot be negative here and the model stops at 10 miles.
C = 4 + 1.5(0) = 4 — The smallest input gives the smallest output.
C = 4 + 1.5(10) = 19 — The largest allowed input gives the largest output.

Answer: Domain: 0 to 10 miles. Range: £4 to £19.

Worked example: Excluded Values in a Rational Function

For f(x) = 1/(x - 2), state the domain and explain the excluded value.

x - 2 — The denominator cannot equal zero.
x - 2 = 0 so x = 2 — At x = 2 the function would be undefined.
All real values of x except 2 — This is often written as x ≠ 2.

Answer: Domain: all real x with x ≠ 2.

7. Common Pitfalls

Reading f(3) as f times 3
Listing outputs as the domain and inputs as the range
Ignoring a context restriction such as a distance or time starting at zero

9. Exam Focus

If a question gives a graph or a real context, use that information. Domain and range are often restricted by the model, not just by the algebra.

Sources and content standards

Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-03-25.

Pearson Edexcel International GCSE Mathematics A (4MA1) specification and resources How we check content Report a correction — include this lesson URL

Continue through the topic

Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.

Interpreting Expressions as Functions Composite and Inverse Functions Working with Coordinates in All Four Quadrants Plotting Straight-Line Graphs Topic 3: Sequences, Functions and Graphs topic IGCSE Edexcel Higher pathway

Frequently asked questions

What is the difference between domain and range?

The domain is the set of input values a function is allowed to take. The range is the set of output values produced by the function. Listing outputs as the domain and inputs as the range is a common pitfall.

How do you find the range from a domain?

Use the allowed inputs to find the outputs they produce. For a taxi fare C = 4 + 1.5m with 0 ≤ m ≤ 10, the minimum cost is 4 + 1.5(0) = 4 and the maximum is 4 + 1.5(10) = 19, so the range is £4 to £19.

What is a function in maths?

A function is a rule that gives one output for each permitted input. Function notation, such as f(x), separates the rule from the value produced by a chosen input.

What does f(3) mean?

f(3) means the output of the function when the input is 3, not f multiplied by 3. For f(x) = 2x - 1, f(4) = 2(4) - 1 = 7 and f(-2) = 2(-2) - 1 = -5.

How do you find the domain of 1/(x - 2)?

The denominator cannot equal zero, so set x - 2 = 0 to find the excluded value x = 2. The domain is all real values of x except 2, often written as x ≠ 2.

What is a real-life example of domain and range?

A taxi fare modelled by C = 4 + 1.5m for distances 0 ≤ m ≤ 10 miles has a domain of 0 to 10 miles. The range is £4 to £19, because C = 4 when m = 0 and C = 19 when m = 10.

How does a real context restrict the domain?

A real context can rule out some inputs, such as negative values or impossible lengths. A distance or time usually starts at zero, so the domain is restricted by the model, not just by the algebra.

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