Real Functions

Pure Mathematics — Second Secondary

The idea of a real function

A real function is a relation between a subset of the real numbers and a subset of the real numbers, in which every element of the first set is linked to exactly one element of the second set.
We write the function as f(x) and read it as “f of x”.

Key points

Domainthe set of x-values for which the function is defined, that is, the values we can substitute into the rule.

Rangethe set of output values f(x) as x runs over the whole domain.

Rulethe calculation that turns each input x into one output f(x), for example f(x) = 3x − 5.

Exampleif f(x) = 3x − 5, then f(2) = 3 × 2 − 5 = 1, so the point (2, 1) lies on the graph of the function.

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