Think of a function as a machine
A function takes an input, follows a rule, and gives exactly one output for each allowed input.
For example, the rule f(x) = 2x means multiply the input by two.
- Input: 5
- Rule: Multiply by 2
- Output: 10
We write this as f(5) = 2 × 5 = 10.
Try another input
If the input is 3, then f(3) = 2 × 3 = 6.
The same rule works for every input in its domain.
What makes something a function?
Each allowed input must have exactly one output. Two different inputs can share an output; that is still a function.
Practice
For f(x) = 2x, what is f(7)?
The answer is 14. Try explaining why before checking your work.