A-level · Algebra & functions

Functions, domain and rangeExam-style questions

What a function is and what its domain and range describe. Function notation; the domain as the inputs and the range as the outputs, each in its own letter; the range of a quadratic from the completed square; why a restricted domain needs the vertex and both ends tested; the largest possible domain of a square root or a fraction; and one-to-one against many-to-one.

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7 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
Graphs 1 to 5 below are each shown in full. Each graph includes its end points, which are marked with dots.

Graph 1Graph 2Graph 3Graph 4Graph 5(a) Write down the number of each graph that

(i) does not represent a function,

(ii) represents a one-one function,

(iii) represents a many-one function,

(iv) represents a function that is its own inverse.

(4 marks)
(b) The function f has domain $\{x : -1 \leqslant x < 2\}$ and is given by $f(x) = 8 - x^3$ .

Write down the range of f in set notation.

(2 marks)
Level 4 · 6 marksTry it