The idea

Functions, domain and range

What a function is, the meaning of domain and range, how to find a range (and why a quadratic's is bounded), and one-to-one vs many-to-one mappings.

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Pure · Algebra & functions

Functions, domain and range

What a function is, the meaning of domain and range, how to find a range (and why a quadratic's is bounded), and one-to-one vs many-to-one mappings.

Why it works

Exactly one output

"State the range of

f

" is a two-mark question that students drop far more often than the algebra deserves — because it isn't asking you to compute anything. It asks you to describe the function's behaviour as a whole, and that needs the vocabulary. A function is a rule that takes each input to exactly one output. We write

f(x)

for the output at

x

, or

f: x \mapsto 2x + 1

. Two sets go with it:

the domain — the inputs the function is allowed to take ( $x$ -values),
the range — the outputs it actually produces ( $y$ -values).

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