What a Function Is

Start from zero — the basic math you need before everything else

A function is like a machine: you feed in an input, and it gives back exactly one output. We write it f(x), read aloud as "f of x", where x is the input. For f(x) = 2x + 1, the machine doubles the input and adds one.

You already use functions all day without naming them. A vending machine is one: press B4 and you always get the same snack. A coffee machine: pick "latte", get a latte every time. A microwave: set 30 seconds, it runs for 30 seconds. Same input in → the same single output out. That's the whole idea.

To evaluate a function at a value, put that value in for x everywhere and work it out: f(3) means "use 3 as the input". The rule that makes something a function is "exactly one output". Feed in the same input and you must always get the same single answer back.

▶ What a Function Is
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