2.8

Functions

Cambridge IGCSE Mathematics (0580)  · Unit 2: Algebra and graphs  · 9 flashcards

Functions is topic 2.8 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 2 — Algebra and graphs , alongside Algebraic notation and manipulation, Equations and Inequalities.  In one line: A function is a relationship between a set of inputs (the domain) and a set of permissible outputs (the range) with the property that each input is related to exactly one output.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.  It is a Supplement (Extended-tier) topic, so it appears only on the Extended-tier papers.

The deck below contains 9 flashcards — 3 definitions and 3 key concepts — covering the precise wording mark schemes reward.  Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

A function? Define it in terms of input and output

A function is a relationship between a set of inputs (the domain) and a set of permissible outputs (the range) with the property that each input is related to exactly one output.

Example: f(x) = x + 2 is a function where each input 'x' produces only one output.

Questions this Functions deck will help you answer

Definition Flip

What is a function? Define it in terms of input and output.

Answer Flip

A function is a relationship between a set of inputs (the domain) and a set of permissible outputs (the range) with the property that each input is related to exactly one output.

Example: f(x) = x + 2 is a function where each input 'x' produces only one output.
Key Concept Flip

Explain function notation and provide an example.

Answer Flip

Function notation is a way of writing functions that clearly indicates the input and output. It uses the form f(x), where 'f' is the function name and 'x' is the input.

Example: If f(x) = 3x - 1, then f(2) = 3(2) - 1 = 5.
Key Concept Flip

If f(x) = 2x + 1 and g(x) = x^2, find the composite function f(g(x)).

Answer Flip

To find f(g(x)), substitute g(x) into f(x). So, f(g(x)) = f(x^2) = 2(x^2) + 1 = 2x^2 + 1. Therefore, f(g(x)) = 2x^2 + 1.

Definition Flip

What is the domain of a function?

Answer Flip

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

Example: if f(x) = 1/x, the domain is all real numbers except x = 0.
Definition Flip

What is the range of a function?

Answer Flip

The range of a function is the set of all possible output values (y-values) that the function can produce. It represents the values that f(x) can take.

Example: if f(x) = x^2, the range is all non-negative real numbers.
Key Concept Flip

Explain what an inverse function is and its relationship to the original function.

Answer Flip

An inverse function, denoted f⁻¹(x), 'undoes' the original function f(x). If f(a) = b, then f⁻¹(b) = a. The domain of f(x) is the range of f⁻¹(x), and vice-versa.

Key Concept Flip

Find the inverse function of f(x) = x - 5.

Answer Flip

To find the inverse, let y = x - 5. Swap x and y: x = y - 5. Solve for y: y = x + 5. Thus, f⁻¹(x) = x + 5.

Key Concept Flip

Given the function f(x) = √(x - 2), state its domain.

Answer Flip

For the square root function to be defined, the expression inside the square root must be non-negative. So, x - 2 ≥ 0, which means x ≥ 2. Therefore, the domain is x ≥ 2.

Key Concept Flip

Describe how to determine if a graph represents a function.

Answer Flip

Use the vertical line test. If any vertical line intersects the graph at more than one point, the graph does not represent a function. This is because a single x-value would correspond to multiple y-values.

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2.7 Straight line graphs 2.9 Differentiation

Key Questions: Functions

What is a function? Define it in terms of input and output.

A function is a relationship between a set of inputs (the domain) and a set of permissible outputs (the range) with the property that each input is related to exactly one output.

Example: f(x) = x + 2 is a function where each input 'x' produces only one output.
What is the domain of a function?

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

Example: if f(x) = 1/x, the domain is all real numbers except x = 0.
What is the range of a function?

The range of a function is the set of all possible output values (y-values) that the function can produce. It represents the values that f(x) can take.

Example: if f(x) = x^2, the range is all non-negative real numbers.

More topics in Unit 2 — Algebra and graphs

Functions sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

2.1 Algebraic notation and manipulation

9 flashcards
2.2 Equations

9 flashcards
2.3 Inequalities

9 flashcards
2.4 Sequences

18 flashcards
2.5 Quadratics

9 flashcards
2.6 Graphs of functions

9 flashcards
2.7 Straight line graphs

9 flashcards
2.9 Differentiation

9 flashcards

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

function f(x) input output domain range composite function inverse function function notation mapping

Key terms covered in this Functions deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

Function? Define it in terms of input and output
The domain of a function
The range of a function

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How to study this Functions deck

Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.