Functions and relations (domain and range) — KCSE Mathematics

KCSE Mathematics · 96 practice questions · 4 syllabus objectives

32 easy34 medium30 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Define a relation and a function; determine the domain and range of a function from a set of ordered pairs, mapping diagram or equation

Distinguish between one-to-one, many-to-one and one-to-many mappings; determine which are functions

Find the composite function fg(x) and the inverse function f⁻¹(x) for simple functions

Functions and relations (domain and range)

Sample Questions

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1
easySHORT ANSWER3 marks

Let the function f(x) = x² + 2 for x ≥ 0. (a) Find f(4). (b) State the range of f(x). (3 marks)

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Part (a) — 1 mark
f(4) = 4² + 2 = 16 + 2 = 18 (1 mk)
Part (b) — 2 marks
Range is [2, ∞) since f(x) = x² + 2 for x ≥ 0 (1 mk)
Minimum value occurs at x = 0, f(0) = 2 (1 mk)
2
easySHORT ANSWER2 marks

Identify the type of mapping represented by the function f(x) = 2x + 3. Explain your reasoning. (2 marks)

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Part (a) — 2 marks
f(x) is a one-to-one function because each input x produces a unique output f(x) (1 mk)
No two different x values yield the same f(x), satisfying the one-to-one condition (1 mk)
3
easySHORT ANSWER3 marks

Identify whether the relation defined by the set of pairs R = {(1, 2), (2, 3), (3, 4), (1, 5)} is a function. Justify your answer. (3 marks)

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Part (a) — 3 marks
R is not a function because the input 1 is mapped to two different outputs (2 and 5) (1 mk)
A function must have a unique output for each input (1 mk)
Thus, the mapping fails the definition of a function (1 mk)
4

A function f is defined by the set of ordered pairs f = {(1, 2), (2, 3), (3, 4), (4, 5)}. (a) State the domain of f. (b) Determine the range of f. (2 marks)

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