Glossary

Functions – Key Terms & Definitions

Essential functions vocabulary for IGCSE Mathematics (0580). Each term includes a clear definition and example to help you understand and remember key concepts.

function

Extended

Rule that maps each input to exactly one output

Example

f(x) = 2x + 1

domain

Extended

Set of valid input values

Example

All real numbers except x=0

range

Extended

Set of possible output values

Example

$f(x) = x^2 \text{ has range } y \geq 0$

composite function

Extended

Function applied after another

Example

fg(x) = f(g(x))

inverse function

Extended

Reverses the original function

Example

$f^{-1}(x) \text{ undoes } f(x)$

mapping

Extended

How inputs relate to outputs

Example

x → 2x + 1

one-to-one

Extended

Each input gives unique output

Example

f(x) = 2x + 1 is one-to-one

many-to-one

Extended

Different inputs give same output

Example

$f(x) = x^2 \text{ maps } \pm 3 \text{ to } 9$

input

Extended

Value fed into a function

Example

x in f(x)

output

Extended

Value produced by a function

Example

f(3) = 7 means 7 is output

notation

Extended

$f(x) \text{ means function } f \text{ applied to } x$

Example

$f(x) = x^2$

self-inverse

Extended

Function that is its own inverse

Example

$f(x) = \dfrac{1}{x} \text{ is self-inverse}$

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Frequently Asked Questions

How many functions terms do I need to know for IGCSE?

This glossary covers 12 key functions terms. Focus on understanding definitions and being able to use each term in context during exams.

Are these terms for Core or Extended?

Terms are labelled as Core or Extended. Core students should focus on Core-labelled terms, while Extended students need to know all terms.

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