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
The function $f$ is defined by $f(x) = x^2 - 1$ . Find $f(-3)$ .
Level 2 · 1 markTry it
2
The function $f$ is defined by $f(x) = 2x + 3$ . Find $f(4)$ .
Level 2 · 1 markTry it
3
The function $f$ is defined by $f(x) = (x - 2)^2 + 3$ . Write down the minimum value of $f(x)$ and the value of $x$ at which it occurs.
Level 3 · 2 marksTry it
4
The function $f$ is defined by $f(x) = 5 - 2x$ . Find the value of $x$ for which $f(x) = 1$ .
Level 3 · 2 marksTry it
5
The function $f$ is defined by $f(x) = x^2 + 1$ for all real $x$ . State the range of $f$ .
Level 3 · 2 marksTry it

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